Relaxation Techniques

Relax Your Mind

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C Relaxation algorithms

Another approach, widely used in remote sensing, is the relaxation method originally applied to the temperature retrieval problem by Chahine (1968). In the development of this algorithm it is assumed that measurements are available at a discrete set of wavenumbers, vi (i 1, m), which are associated with a set of weighting functions W(v,, z) whose maxima are well distributed over the atmospheric levels of interest. A first estimate of the temperature profile is obtained from the relation to these temperatures. The solution is then iteratively improved using the relaxation algorithm

Large interstellar molecules

Medium of galaxies as a whole, and star burst galaxies - are dominated by broad infrared emission features (Fig. 1.7). These IR emission features are characteristics for polycyclic aromatic hydrocarbon (PAH) materials. These bands represent the vibrational relaxation process of FUV-pumped PAH species, containing some 50 C atoms. These species are very abundant, 10-7 relative to H, locking up about 10 of the elemental carbon.

Overcoming Incoherences

The fundamental reason which makes usual fluids smooth is that the fluctuations are damped by molecular chaos. Fluctuations are erased as long as the molecular relaxation time is much shorter than all the macroscopic time-scales. In a supersonic turbulent medium the non-linear convective term of fluid equations on the contrary exacerbates discontinuities, that is, shocks. Since turbulence is multi-scale, these shocks occur and interact with each other at all scales. The medium has all the grounds to constantly grow discontinuities. Then the justification of using differential equations for smooth flows in hydrodynamics is lost.

From the Sun to the edge of the Solar System

The magnetosphere of Jupiter is another wonderful laboratory for studying how plasmas behave in space.With its rapid rotation, strong magnetic field and internal sources of plasma, it has been compared to binary stellar systems and even pulsars. It is the most accessible environment for studying some further fundamental processes such as the plasma's interactions with neutral gas and with the planet's moons, magnetodisc stability, the relaxation of rotational energy and associated energetic processes,and the loss of angular momentum by magneto-plasma interactions.The last two processes are important in understanding accretion mechanisms that lead to the formation of planetary systems. A group of at least three spacecraft operating together with an optimised plasma payload,as part of a Jupiter exploration programme, will permit the first fundamental advances in understanding the structure and dynamics of this fascinating plasma environment.

Galaxy Clusters Now and as they were at Moderate Redshift

Rich clusters of galaxies are the largest collapsed structures we can observe, and perhaps model successfully. Clusters can be studied as a group by calculating their integrated X-ray or optical luminosity functions, and their galaxy type distributions. One may also gain insight into their mass and degree of relaxation by modeling individuals as large collections of test particles in cosmic simulations. The abundance of massive clusters can provide a constraint on the matter-content of the Universe.

Optical Analysis Of Cluster Mergers

Abstract An increasing amount of data has revealed that many clusters are very complex systems. Optical analyses show that several clusters contain subsystems of galaxies, suggesting that they are still in the phase of dynamical relaxation. Indeed, there is a growing evidence that these subsystems arise as the consequence of group cluster mergers. We here review the state of art of optical search and characterization of cluster substructures. We describe the effects cluster mergers have on optical measures of cluster dynamics, and on the properties of cluster member galaxies. We also discuss cluster mergers in relation to the large scale structure of the universe.

The Ecology of Dense Star Clusters with Binaries

We study the first 100Myr of the evolution of isolated star clusters with 117965 single stars and 13107 primordial hard binaries. Our calculations include stellar and binary evolution. The early evolution of these clusters can be characterized by three distinct phases, which we dubbed A, B and C. Here phase A lasts for the first 3 Myr and is dominated by two-body relaxation, phase B lasts to about 20-100 Myr and is dominated by stellar mass loss, after that phase C sets in, which again is dominated by two-body relaxation. The presence of the primordial binaries has little effect on these various stages, nor on the other conclusions we draw here. The mass function of the main-sequence stars in the core becomes as flat as x 1.8 (initial Salpter was x 2.35), and in the outer 10 (by mass) of the cluster the mass function exponent is as steep as x 2.6. Over the lifetime of the star cluster, a large number of stellar-mass black holes and neutron stars are formed. Roughly 50 -70 of...

Extrapolations of Surface Magnetic Fields

Numerical methods for solving the full nonlinear force-free equations have been developed. To ensure a well-posed problem, one needs a measurement of the vertical component of the magnetic field everywhere and the value of a(r) at the boundary for one polarity. Relaxation techniques have had considerable success at producing an accurate solution to the equations, as judged by comparisons with observed magnetic field lines (Jiao, McClymont, & Mikic 1997) and measured coronal magnetic field strengths (Lee et al. 1998), but there are some limitations the direction of the transverse component of the magnetic field in the corona cannot be determined unambiguously (to within 180 ) (e.g., Semel & Skumanich 1998) errors in measurements of the photospheric magnetic field affect the reconstruction of the coronal field (Klimchuk & Canfield 1994) and the photospheric values of a may not be appropriate in the corona since the photosphere is not force-free (Metcalf et al. 1995). In the future...

Black Hole and Neutron Star Retention

The solid curves in the bottom panel of Fig. 5 show an interesting depression between about 75 Myr and 80 Myr. It appears that the binaries with a white dwarf located within 2 rcore become depleted. This is not really the case, but rather the cluster experiences a phase of core collapse. This may not be so surprising at first, if one imagines that core collapse tend to happen in about 15 -20 of the half-mass relaxation time 12 . For this cluster, the half-mass relaxation time is about 440 Myr and the core collapse is therefore expected at an age of about 65-85 Myr, which is consistent with the moment of core collapse in simulations without primordial binaries.

Dynamic Perturbations

As discussed in Section 2, any dynamic perturbation could cause current sheet formation along the BPSS or in the vicinity of the X-line. Indeed, Torok et al. (2004) found that the X-line pinched into a current sheet even during the relaxation of the approximate analytical equilibrium of Titov and Demoulin (1999, hereafter T&D) to a nearby stable numerical equilibrium. Similarly, Fan and Gibson (2006) found that, even during the quasistatic evolution of the a confined flux rope before its eruption, sigmoid current sheets formed along the BPSS. These topologies present a fault line in the coronal magnetic field across which field lines behave very differently when driven dynamically. Thus, many different perturbations, ranging from flux emergence to photospheric motions at the footpoints of the field lines, may constantly cause the development of magnetic tangential discontinuities (or current sheets) where reconnections heat persistent, or long-lived sigmoids.

Quantitative Classification Of Global Morphology

The presence of substructure in clusters implies they are still forming and evolving dynamically, and thus a logical candidate for a fundamental parameter is the current dynamical state. The dynamical state of a cluster is related to the amount of time required for the cluster to virialize i.e., a time of order a crossing time. But for a cluster of a given total mass one can imagine many different morphological configurations - and formation histories - that would lead to similar relaxation timescales. Hence, to classify clusters having different formation histories but similar dynamical states we also require one or more fundamental parameters to specify the type of merger (e.g., bimodal, many small subclusters) as indicated qualitatively by the classes of Jones & Forman (1992).

On the Possible Occurrence of Astigmatism in Star Tests

Temporary astigmatic distortion of the main mirror can be due to a variety of causes but principally three uneven thermal expansion contraction in changing temperatures, pinching or stressing of the disk due to overtight clamping or fit in the mirror cell, and flexure of an inadequately supported disk under its own weight. Thermal effects can easily, and frequently do, bring about a miraculous transformation of a very good mirror into one for which there are no words in polite society unfortunately it never works this alchemy in reverse If afflicted with this malady, there is nothing for it but to pack up for the time being while thermal relaxation takes its course or, perhaps, to pass the time with some undemanding low-power sightseeing. One can, however, take common-sense precautions to avoid those recipes which create the problem in the first place, the two worst and commonest being indoor storage at, say, 20-25 C of an instrument that may be called into play at a moment's notice...

Method and Assumptions

We use a Monte Carlo method described in detail in 6 . This method assumes a static cluster background, all relevant dynamical parameters being kept constant throughout dynamical simulation. In particular, the cluster model we consider here has central density nc 105 pc 3 , velocity dispersion a 10 km s , escape velocity vesc km s and half-mass relaxation time trh 109 yr . The code takes into account such important dynamical processes as mass segregation and evaporation, recoil, physical collisions, tidal captures,

Dust Heating and Destruction

We mentioned previously that the emissivity of the postshock gas is sensitive to its state of ionization. For increasing shock velocity, first hydrogen and then the heavy elements become completely ionized and therefore ineffective as coolants. Suppose that the depth of the relaxation region is limited by some constraint, such as the geometrical thickness of the shocked cloud. Then there exists a critical shock speed above which the postshock gas cannot cool in the available flow time. The energy injected by the preshock gas thus remains trapped for an extended period. Such nonradiative shocks are created, for example, by the impact of O- and B-star winds on surrounding cloud matter, a circumstance we shall consider in Chapter 15.

Heating and Cooling Mechanisms

Within a J-shock, the immediate postshock temperature follows from the Rankine-Hugoniot jump conditions, while the subsequent decline in the relaxation region is due to the various cooling mechanisms already discussed. In a C-shock, both the temperature rise and decline are smooth and, as we have seen, cover a larger total distance. The temperature profile depends sensitively on both the internal heating and cooling. Nevertheless, the jump conditions may still be used to relate upstream and downstream material outside the interaction region, i. e., in which both charged and neutral species have a common speed and kinetic temperature. Heating within the shock mainly stems from the differential velocity between the ions and neutrals. This slip generates random motion in the neutral atoms and molecules, as a result of repeated scattering.

Box 22 The Nature Of The Heliospheric Boundary Regions

The Knudsen number, Kn, is the ratio X L, where X is the mean free path of neutral atoms and L is a characteristic macroscopic length scale, such as the size of the solar heliosphere, 100 AU. It is a measure of the neutral distribution relaxation distance and is 1 inside the heliosphere and 1 in the very local interstellar medium. Thus, within the heliosphere neutral and plasma distributions cannot equilibrate and may possess quite distinct bulk flow speeds and temperatures. Charge exchange between the coupled, nonequilibrated neutral and charged particle populations can therefore introduce distinct new populations of neutral atoms and plasma whose characteristics reflect their parent population. The subsequent interaction and assimilation of the newly created plasma and neutral populations into the existing plasma and neutral distributions may then lead to the substantial modification of the overall partially ionized plasma system. Thus, the total neutral distribution cannot relax to...

The timescale of star cluster formation

Such long formation timescales would also allow for significant dynamical relaxation of the forming star cluster for N equal mass stars the relaxation time is treiax 0.1N (lnN)tdyn, i.e. about 14 crossing timescales for N 1000. Using numerical experiments, Bonnell & Davies (1998) found that the mass segregation time (of clusters with mass-independent initial velocity dispersions) was similar to the relaxation time. The presence of gas should shorten these timescales (Ostriker 1999). Therefore at least a part of the observed central concentration of massive stars in the Orion Nebula Cluster, in particular the Trapezium stars, may be due to mass segregation rather than preferential formation at the center.

Familial and Personal Tensions

To provide a place where all could come together on occasion for relaxation, a group of employees developed a recreation area five kilometers east of Highway 3 on KSC, halfway between headquarters and the residential area farther south on Merritt Island. Situated on the west bank of the Banana River, with 762 meters of shore line and a boat basin, the tract, one kilometer square, boasted a setting of live oak, palm, persimmon, and pine trees, and provided playgrounds, picnic areas, and a swimming area.50 The Spaceport Travel Club also organized a year-round series of trips that specialized in Caribbean cruises and air journeys to Europe, Hawaii, and the Orient. In spite of these efforts, the KSC employees remained segmentized, close to their own division or contractor, united only in the purpose of sending men to the moon and bringing them back.

Impact Activity And Chronology

Comparative studies of the morphology of impact structures on the smallest terrestrial planets has provided some insight into the nature of Mercury's crustal processes (Potts et al, 2002). Basins on the Moon and Mercury apparently experienced an analogous sequence of events, scaled by gravity, following formation of a transient cavity, which induced uplift, followed by isostatic relaxation, and volcanic infilling. Multi-ring basins on all three bodies have a similar ring spacing (Potts et al, 2002). Based on the size of transient cavities and density of impact basins (Melosh, 1982), Mercury's early crust was most like the lunar farside, but more viscous than the lunar or martian crusts (Potts et al, 2002). Because it was also hotter, a dryer crust is also implied.

NGC 3656 and Other Elliptical Galaxies in the Sample

NGC 3656 is the far-infrared (FIR)-brightest elliptical in our sample. It has an optical elliptical body with an obscuring north-south, galactic minor-axis, edge-on gaseous dust lane (see right panel of Figure 1), two tidal tails, a system of shells and counter-rotating cores. These features together have been interpreted as evidence that the NGC 3656 system is an early major-merger remnant of disk galaxies (cf. Balcells 1997, 2001). Central structures that are seen in unsharp-masked and residual galaxy-model K-band images of NGC 3656 have recently been interpreted as qualitative evidence that phase-mixing, since the disk-disk merger and subsequent violent relaxation of this galaxy, is incomplete (Rothberg & Joseph 2004).

Total Dose And Structural Damage Effects Experimental Simulation

1019.5 and includes the moderate dose rate irradiation followed by 100 oC 168 hours annealing (Fleetwood et al., 1991). This method does not deal with any specific property of the device-under-test, it is rather simple in practice and is declared to be usable for hardness assurance for all CMOS IC in low and moderate dose rate environment. From the other hand, the procedure is excessively conservative respecting to the low dose rate environment that may lead to hardness underestimation which may be crucial for commercial IC's. Besides, the unified accelerated test conditions (annealing temperature and duration) do not guarantee the complete relaxation of radiation-induced charge within the specified time period, especially taking into consideration the latent processes. The second approach to IC's low dose rate response prediction includes the evaluation of MOS or bipolar electrical model degradation parameters and specifying of irradiation mode to simulate low dose irradiation...

Simplest and Most Fundamental Flares

Thus, at least in some cases, flares are not simply due to a relaxation process. This situation is similar to magnetospheric substorms. The solar wind must drive the magnetosphere to cause magnetospheric substorms, providing the power e VB2sin4(0 2)lo2, instead of a simple relaxation process in the magnetotail. In fact, the total magnetic flux in the magnetotail can increase during substorms (Chapter 4), but a substorm ends when e starts decreasing.

Multistructure interpolation methods chain locally updated planes selfpenalty walk conjugate peak refinement and nudged

The methods in this section operate with multiple (more than two) structures or images connecting the reactant and product, and are often called chain-of-state methods. Relaxation of the images will in favourable cases not only lead to the saddle point, but also to an approximation of the whole reaction path. The initial distribution of structures will typically be along a straight line connecting the reactant and product (LST), but may also involve one or more intermediate geometries to guide the search in a certain direction.

Interactions and AGNStarburst Activity 51 Basic Physics of Major Mergers

In the final stages of the merger, as the galaxies merge and undergo violent relaxation, the gas experiences rapidly varying gravitational torques as well as shocks on interacting orbits (e.g., Mihos & Hernquist 1996), and therefore loses energy and angular momentum. Large gas inflows 5. After violent relaxation, the end-product of a major merger tends to have an r1 4 de Vaucouleurs-type stellar profile and boxy isophotes similar to many luminous elliptical galaxies. In the case of intermediate mass ratio (e.g., 1 3) mergers, the gas has a larger specific angular momentum and tends to settle into an extended inner disk (Naab & Burkert 2001) rather than being as centrally concentrated as in a 1 1 merger. The stellar component has an r1 4 profile, disky isophotes, and isotropic velocity dispersion similar to lower luminosity disky ellipticals (Naab & Burkert 2001).

Halo Shapes Dynamics and Environment

In the hierarchical structure formation model cosmic halos are supposed to form by accretion of smaller units along anisotropic direction, defined by large-scale filamentary structures. After the epoch of mass aggregation (which depend on the cosmological model), violent relaxation processes will tend to alter the halo phase-space configuration producing quasi-spherical halos with a relatively smooth density profiles.

Impact of Stratospheric Heating on the Troposphere of a Simplified GCM

The model climatology consists of a single jet which extends through the depth of the troposphere in the mid-latitudes of each hemisphere, maintained by fluxes of (heat and) momentum associated with the transient weather systems (shown later). The observed climate (Figure 1c) comprises an eddy-maintained jet in each hemisphere, and also a subtropical jet which is confined to the upper-troposphere of the winter hemisphere, and which is only partially separated from the eddy-maintained jet. The existence of, and variations in, the subtropical jet involve moist tropical processes which have been idealised as a linear relaxation in the simplified model. The model results are therefore relevant only to stratospheric influences on the eddy-driven mid-latitude jets and not to other possible mechanisms such as changes in convective activity or the vertical propagation of stationary planetary waves, such as discussed by, e.g., Rind and Balachandran (1995).

Liouville Dark Energy the End Game

In the generic class of non-critical string models described in this talk, the a model always asymptotes, for long enough cosmic times, to the linear-dilaton conformal a-model field theory of 12 . However, it is important to stress that this is only an asymptotic limit, and the current era of our Universe should be viewed as close to, but still not at the equilibrium relaxation point. Thus the dilaton is almost linear in the a-model time, and hence varies almost logarithmically in the Einstein-frame time (8). This slight non-equilibrium would lead to a time dependence of the unified gauge coupling and other constants such as the four-dimensional Planck length (1), mainly through the time-dependence of the string coupling (9) that results from the time dependence of the linear dilaton (3). where, for large tE, Q is given in (29) and approaches its equilibrium value q0, and we took into account (30). Thus, the dark energy density relaxes to zero for tE to. Notice an important feature of...

Protoclusters And Starforming Regions

Young clusters offer the further advantage of being largely free of the effects of dynamical evolution. Some degree of mass segregation exists in even the youngest systems, with the highest-mass stars often more centrally concentrated than the average cluster member. Given typical crossing times of between a few x105-106yr, this concentration is more likely to be a result of the conditions prevailing during the earliest stages of star formation rather than a consequence of dynamical relaxation. Solar-type and lower-mass stars appear to follow nearly identical radial density distributions (as in the Pleiades), thereby minimising potential biases due to incomplete areal coverage.

Flow topology and jet thermodynamics

The ratio of the stress relaxation time of the fluid to a representative timescale for the flow (such as the rotation timescale in this case) is variously called the Weissenberg number or the Deborah number. If we keep the Reynolds number low but gradually increase the Weissenberg-Deborah number, the secondary (i.e. meridional) flow reverses to the flow qualitatively sketched in Figure 34.1-B, as the elastic hoop-stresses begin to dominate the inertial forces.

An Xray View of the Cores of Galaxy Groups Effects of AGN and Mergers on the IGM

Using data from XMM-Newton and Chandra, we have studied a number of X-ray luminous galaxy groups in order to investigate the effects of mergers and AGN activity on their properties. We here present results from four disturbed systems with particularly interesting features. These groups provide examples of AGN heating preventing runaway cooling and mixing enriched gas from the dominant elliptical with the surrounding intra-group medium. We also show that under standard assumptions of hydrostatic equilibrium and relaxation, X-ray analysis may underestimate the gravitational mass of disturbed systems.

The Closest of the Close Observational and Modeling Progress

Two of today's most critical unresolved problems in binary star research are the formation and structure of W Ursae Majoris binaries. Demands imposed by nearly equal effective temperatures for the two stars lead to a grossly different mass-luminosity relation from that of single main sequence stars. That only non-equilibrium models can account for many W UMa properties is widely recognized. One such model is the thermal relaxation oscillator model, in which systems oscillate between states of good thermal contact and broken contact. Notwithstanding decades of theoretical research, W UMa's have not been fitted into a comprehensive structural theory, and the formation mechanism also needs to be resolved. The recent idea that all W UMa's are part of triple (or multiple) systems and formed through dynamical interactions with third bodies may well answer that question. On the observational front, we have seen in the last decade a vast increase in the number of double-lined systems with...

Dynamic arcade models

In this context a question has been raised about the appropriate minimum energy state reached by relaxation via reconnection. As mentioned above, Taylor relaxation would result in the linear force-free field (see also Section 11.5.3) consistent with the boundary condition. However, this requires that all flux tubes participate in the reconnection. It was pointed out Hu et al. (2003) used a relaxation method to find force-free equilibria numerically. A low-lying flux rope is introduced into a dipolar or partly open potential field. The configuration either relaxes into a stable equilibrium without significant rising of the flux rope or the flux rope erupts catastrophically to infinity forming a corresponding current layer. What type of behaviour takes place depends on the energy the eruption occurs if the process is energetically possible.

Theory of Star Cluster Evolution

Now that we have set the stage and discussed the tools and the techniques we can continue by discussing the global evolution of star clusters, which is characterized by three quite distinct phases these are subsequently A the early relaxation dominated phase, followed by phase B in which the 1 (by number) most massive stars quickly evolve and lose an appreciable fraction of their mass. Finally, phase C starts when stellar evolution slows down even more and relaxation takes over until the cluster dissolves. To complete the list we can define phase D which is associated with the final dissolution of the cluster due to tidal stripping, but we will not discuss this phase in detail. In the following discussion we assume, for clarity, that the location in the cluster where the stars are born is unrelated to the stellar mass i.e., there is no primordial mass segregation. In that case, the early evolution of the star cluster is dominated by two-body relaxation, or to be more precise by...

Black Holes in Star Clusters

Young star clusters, with a half-mass relaxation time trt 100 Myr are, as we discussed in 8.2.1, prone to dynamical friction, and therefore are likely to experience core collapse before stellar mass loss drives the expansion of the cluster. Realistic clusters have a broad range in initial stellar masses, generally from mm n 0.1 Mq to mmax 100 Mq. Adopting such a mass function as a condition at birth, the mean mass (m) ranges then from (m) 0.39 Mq (Salpeter 1955) to about 0.65 Mq (Scalo 1986), depending on the specific mass function adopted. Here I like to stress that there is a large variety of initial mass function available apart from the two above mentioned there are the Miller & Scalo (1979), Kroupa, Tout, & Gilmore (1990) with some adjustments for high mass stars and Kroupa & Weidner (2003, see also Kroupa, 2001). These mass functions seem to differ quite substantially, but for the dynamical evolution of the cluster they do not make a big difference, as for this process it is the...

Experimental Studies of UVinduced Dusty Plasmas under Microgravity

The first stage of the experiment was confined to observing the behavior of the ensemble of macroparticles placed in the ampul under the action of solar radiation. In the initial state the particles were on the walls of the ampul therefore, the experiment was carried out according to the following scheme a dynamic disturbance (jolt) of the system and relaxation to the initial state, i.e., drift to the wall. Figures 2a,b show the successive states of the system of particles in the ampul with P 0.01 Torr following dynamic disturbance of the system, and Figs. 3a,b show the state of the system in the ampul with P2 40 Torr. Observations of the motion of the particles showed that the velocity vectors of the particles are randomly directed in the initial stage and that the particles drift to the walls without a preferential direction. Subsequently, a preferential direction usually appears, but motion along definite trajectories is displayed more strongly in the vessel with the higher...

Particle Acceleration in Reconnection

Most of the fast plasma flows observed in space and astrophysics are believed to be caused by mechanisms similar to a plasma gun. One of these mechanisms is magnetic reconnection, where the applied electric field is the induction field caused in the reconnection process, and the acceleration of the plasma reaches energies of the order of the Alfven energy. For example, the fast solar wind outflow during solar flares reaches velocities of the order of 1000 km s, which are the range of fast reconnection speeds in the lower corona. Optical line observations during flares have demonstrated one-sided broadening of the lines, which are successfully interpreted as Doppler broadening due to bulk acceleration in reconnection of the antiparallel magnetic field lines in coronal magnetic arcades. Similarly, fast flows in the magnetotail of the Earth's magnetosphere are interpreted as result of reconnection in the tail current sheet. Hence, although the reconnection process is not yet...

Accelerated Distributions

The shape of the right-most distribution function is clearly unstable and will lead to relaxation of the beam into a gradual distribution function. Many observations in space have shown that the final distribution functions which result after such a relaxation process is some kind of power law distribution with negative power law index. An There is no general theory for the power law index, k, of the kappa distribution, rather this index depends on the process which generates the beam and on the follow-up process which relaxes the beam. Because these processes are both nonlinear, they depend on the properties of the plasma, the conditions for instability and relaxation. It seems, however, that such distributions with different k are a very general property of plasmas and are encountered in almost every place, where strong interaction between plasma and turbulence is observed.

The Double Slit Experiment

If you make two slits in a screen then after a certain relaxation time (it must be taken to be very fast) the medium will enter a new mode, that is, reorganize itself into a new co-operative state. The exact new state or mode will depend on the size of the slit and the distance between the slits, not on the material of the slit (e.g., paper or lead). If you block one slit or the other then the mode would be different than if both were open. It is more important here to imagine that the slits determine the way the medium can interact with itself to enter a new stable state or mode. A photon (or electron or neutron) passes through one slit only. It 'knows' if the other slit is open or closed from the global mode of the medium. The medium would be in a different mode if only one slit was open. It is being guided by the pattern in the medium.

Close Binary Supersoft XRay Sources CBSS

A particularly detailed long-term time-variability study has been performed on the LMC CBSS RX J0513.9-6951. Figure 12.10 shows the result of the ROSAT HRI and optical monitoring throughout the X-ray bright interval along with the optical data folded over the cycle length 72 . The monitoring revealed the existence of quasi-regular X-ray and optical high and low states of opposite sense, suggesting that the underlying clockwork is a relaxation process. About 120 days of an optical high and X-ray off state are followed by a sharply defined 40-day optical low and X-ray on state. The oscillating behavior of RX J0513.9-6951 has been interpreted as a limit cycle brought about by variations of the accretion rate around Mcrit. The Reinsch et al. model 72 is based on the viscous time scales for the irradiation-induced drainage of the outer accretion disk and the refilling of the inner disk hole created by the expanded white dwarf envelope. In this model, the mass transfer rate from the...

Spacelab Medical Development Test I

SMD hardware used during the 1977 simulation, with support consoles, showing the attached Shuttle mock-up mid-deck used by the crew for rest and relaxation. SMD hardware used during the 1977 simulation, with support consoles, showing the attached Shuttle mock-up mid-deck used by the crew for rest and relaxation.

Schmidt Correctors and Diffraction Gratings Aspherized by Active Optics

Elf Hat Template For Cut Out

The methods developed for refractive plate correctors have been called elastic relaxation figuring or more commonly stress figuring. B. Schmidt used the classical method by zonal retouch for making his corrector plate (in Chap. 4 8 ).1 The handwritten elasticity formulas found in Schmidt's personal papers all concern the flexure of beams.2 Though these formulas are not directly applicable to circular plates, he clearly emphasized that a much smoother profile could be obtained by surfacing a plate bent by partial vacuum while supported at its edge. Proposed by Schmidt as an aspherization concept for obtaining the best profile continuity, the elastic relaxation method - or stress figuring method - is now widely known as the basic method of active optics.

Particle Acceleration in Secondary Flare Loops

The quadrupolar configuration (Figure 1, right-hand side) involves magnetic reconnection between two closed magnetic field lines, which relaxes into an alternative quadrupolar connection with switched polarities. This basic (3D) quadrupolar reconnection process has also been dubbed as a flaring process between two interacting loops and was physically interpreted as a magnetic flux transfer between two current-carrying loops (Melrose, 1997). Observational evidence for this type of reconnection was obtained from the detailed analysis of magnetic polarities at the flare loop footpoints (Hanaoka, 1996, 1997 Nishio et al., 1997) and the 3D reconstruction of the magnetic field topology (Aschwanden et al., 1999). In most of the cases observed by Hanaoka (1996, 1997) and Nishio et al. (1997), the secondary large-scale flare loop showed a brightening in soft X-rays and microwaves (see the four cases in Figure 2), simultaneously with the bright hard X-ray and soft X-ray emission in the primary...

Multi Configuration Self Consistent Field

MCSCF methods are rarely used for calculating large fractions of the correlation energy. The orbital relaxation usually does not recover much electron correlation, and it is more efficient to include additional determinants and keep the MOs fixed (CI) if the interest is just in obtaining a large fraction of the correlation energy. Single-determinant HF wave functions normally give a qualitatively correct description of the electron structure, but there are many examples where this is not the case. MCSCF methods can be considered as an extension of single-determinant methods to give a qualitatively correct description.

Deep Sky Observatory

Dome Forms Building

I designed and built the 4.8 m (16 ft) dome myself, after regular work hours and on weekends. I was up against a rather gruelling time schedule of thirty days from start to finish. This was due to a number of factors. First, the unexpectedly fast sale of our previous home (which we needed to sell in order to free up money for the new one) had forced us into rental accommodation on only three weeks' notice. Second, the new construction progressed quickly, and any delay in the dome would cost our building contractor lost time (and us more money). So the dome had to be completed, delivered and ready for lifting by crane on the same day that the roof trusses were put into place. Finally, just to add to the excitement, we were ticketed to leave for the solar eclipse in Baja, California only a day or two after the scheduled lift. There was no margin for relaxation

The shock spectrum and shock diagnostics

The total intensity of the cooling lines in a radiative shock is Itot p0v3 4 (assuming isotropic emission). For high velocity shocks (v 60 km s-1), much of the shock energy will ultimately emerge as HI Lya photons, which are resonantly scattered and eventually absorbed by dust over a column of some 1020 cm-2 (cf. Section 7.2.4). Note that the preshock gas is velocity shifted by 3 4vs to vs relative to the Lya-emitting postshock gas, which complicates the radiative transfer. The Lya photons can also be absorbed in the postshock relaxation layer and hence Lya diffusion can influence the shock structure. The hydrogen and helium optical lines are produced by recombination and, hence, their spectrum will be similar to that of photo-ionized gas. In the optical range, shock-ionized regions can be distinguished from photo-ionized gas (HII regions) through their strong lines from low excitation species such as OI (6300 A and 63 m), OII (3727 and 3729 A), NI (5198 and 5200 A), NII (6548 and...

Value Problems Using Generating Functions Theory and Applications to Astrodynamics

For a general Hamiltonian dynamical system, a two-point boundary value problem is generally solved using iterative techniques such as shooting and relaxation methods. The shooting method 5, 29 consists of choosing values for all of the dependent variables at one boundary. These values must be consistent with any boundary conditions for that boundary, but otherwise are initially guessed randomly . After integration of the differential equations, we in general find discrepancies between the desired boundary values at the other boundary. Then, we adjust the initial guess to reduce these discrepancies and reiterate this procedure again. The method provides a systematic approach to solving boundary value problems, but suffers several inherent limitations. As summarized by Bryson and Ho ( 7 p. 214), Relaxation methods 30 use a different approach. The differential equations are replaced by finite-difference equations on a mesh of points that covers the range of the integration. A trial...

Nonhomologous Evolution

18.2.1 Thermal Relaxation surface layers. But Lcrit) is not just the maximum luminosity that can be carried by radiation. It is also, to the same degree of approximation, the actual interior luminosity within any radiatively stable star. Thus, the pre-main-sequence object of interest is generating, at least initially, more luminosity than it can radiate into space. This imbalance cannot last indefinitely. Both the stellar interior and surface layers must change until Lcrit) and L* match. In other words, the star must undergo thermal relaxation. The interior structure of any star is determined by its run of specific entropy, s(Mr). We recall from Chapter 11 that the specific entropy added, layer by layer, to a protostar tends to increase with time, as a result of the accretion process itself. If deuterium fusion drives global convection, mixing by turbulent eddies enforces a spatially uniform s(Mr), regardless of the star's accretion history. In a radiatively stable object, however,...

Star Aberration Examples On Rc Telescope

Black And White Birch Tree

Single lens correctors In spite of the inevitable chromatic aberrations, such simple correctors can be considered in certain circumstances. Kohler 4.12 4.13 noted that the negative field-flattening lens of the RC telescope can also correct the astigmatism if it is shifted from the image and the as-pheric constants of the mirror system are changed to compensate the coma inevitably introduced by the lens. This is a good practical example of the relaxation (b) in The properties of this corrector, which was manufactured for the ESO 3.6 m quasi-RC telescope and determined the forms of the mirrors, were discussed by Wilson 4.15 . Figure 4.19 reproduces spot-diagrams given for the best focus of the mean wavelength (546 nm) over a Two- and three-lens correctors for quasi-classical Cassegrain telescopes In his pioneer paper of 1949, Wynne 4.23 investigated correctors for classical Cassegrain telescopes. Because of the problems referred to in and, he concluded that a...

Concrete Non Critical String Example Colliding Branes

A scenario in which the collision of two Type-II 5-branes provides inflation and a relaxation model for cosmological vacuum energy. At times long after the collision, the branes slow down and the central charge deficit is no longer constant but relaxes with time t. In the approach of 18 , this relaxation has been computed by using world-sheet logarithmic conformal field theory methods 28 , taking into account recoil (in the bulk) of the observable-world brane and the identification of target time with the (zero mode of the) Liouville field. In that work it was assumed that the final equilibrium value of the central charge deficit was zero, i.e., the theory approached a critical string. This late-time varying deficit Q2(t) scales with the target time (Liouville mode) as (in units of the string scale Ms)

H28n pu22

The phenomenon of particle acceleration in space plasma is, at first sight, in sharp contradiction with the second fundamental law of thermodynamics. Namely, by particle acceleration processes plasma transforms, one would think, into an evidently non-equilibrium state thermal plasma + very small number of accelerated particles with energy density of the same order or much higher than energy density of the thermal plasma. However, as was emphasized by Syrovatsky (1968), there is no contradiction. The matter is that the particle acceleration proceeds during a time that is much smaller than the time of thermal relaxation of space plasma. In fact, the

Multipole expansion

So far, we have been concerned with direct summation methods. This approach inevitably leads to a restriction in the particle number that can be considered. One of the biggest technical challenges is concerned with the simulation of star clusters. Such systems usually develop a core-halo structure with a large range in dynamical time-scale. Thus in the simple theory of relaxation due to stellar encounters, the orbital energy of each star changes at a rate that is related to the inverse square root of the local density. Hence more distant stars move in essentially collisionless orbits as far as nearest neighbour interactions are concerned. This behaviour can be modelled by representing the cluster potential in terms of a multipole expansion based on Legendre polynomials. First the basic formulation as applied to the whole system is given Aarseth, 1967 . This approach is also relevant for other developments in stellar dynamics, such as tree codes Barnes & Hut, 1986 and several related...


The simulated star clusters are initialized by selecting the number of stars, stellar mass function, binary fraction and their orbital elements and the density profile. For our most concentrated model (simulation 1) we adopt the initial conditions derived by Portegies Zwart et al. 14 to mimic the 7-12 Myr old star cluster MGG-11 in the star-burst galaxy M82, which was observed in detail by McCrady et al 11 . In this paper, however, we extend the evolution of this model to about 100 Myr. Subsequent simulations are performed with larger cluster radius, resulting in longer initial relaxation times. The stellar evolution model adopted is based on 1 , and the binaries are evolved with SeBa 16 . For the other simulations 2, 3 and 4, we adopt the same realization of the initial stellar masses, position and velocities (in virial N-body units 5 ) but with a different size and time scaling to the stellar evolution, such that the two-body relaxation time (trh) for simulation 2 is four times that...


Based on a many particle approach the dynamical structure factor for a dusty plasma has been calculated taking into account collective effects as well as collisions. This was achieved using a consistent perturbation expansion based on a generalized linear response theory. The heart of our treatment is the systematic determination of the force-force correlation function which in turn leads to expressions beyond the relaxation time approximation.

Heated H2

Let us finally consider observations of molecular hydrogen. We earlier noted that photodissociation through excitation of the Lyman and Werner bands is an inefficient process, as the excited molecule usually relaxes intact to its ground state. The fluorescent emission accompanying such relaxation is another important signature of photodissociation regions. Radiation from the lower rovibrational transitions occurs at near-infrared wavelengths accessible to ground-based telescopes. If the ambient density nH is subcritical with respect to these transitions (ncr t 106 cm-3), the branching ratios during fluorescent cascade depend only on the transition rates for radiative decay, i. e., on internal molecular constants. Thus, the relative intensities of the various lines are also determined, although the absolute intensities still vary with G0 and nH. Referring back to Figure 5.4, consider the 1 - 0 S(1) and 2 - 1 S(1) lines, which are transitions between the same rotational sublevels for v...

Molecule Formation

The far-infrared and millimeter rotational emission from these molecules, together with increasing thermal contact with the relatively cold dust, allow the cloud gas finally to settle back down to its original, undisturbed temperature. Note that the total postshock cooling time is only a few years for shocks impacting molecular clouds. In the example shown in Figure 8.10, the distance covered by the relaxation region is of order 1013 cm.

Astronomy beckons

For relaxation at the family home on Tomahawk Trail, he enjoyed nothing more than the simple pleasures of gardening. He also took great pride in building a stereo unit for his family, and loved tinkering under the bonnet of an old Triumph sports car he'd bought soon after he and Joan were married. Fond of many outdoor activities, he especially enjoyed ice-skating on Madison's frozen lakes in winter, and had once camped and hiked in the majestic Rockies.

S Mineshige

X-ray time variations of Cyg X-l in the hard state comprise two components with different timescales one characterizing the light variation and the other rapid spectral hardening around the peak. These seemingly indicate two (or more) physical processes being involved e.g., disturbance propagation and magnetic reconnection, leading to magnetic flares. Such features are consistent with the view of MHD accretion flow. The unique properties of the MHD accretion flow are also discussed. To explain the observed X-ray spectral shape and variability during the hard state, magnetic energy needs to be dissipated and be radiated away in short timescales. Finally, we will touch on the peculiar variations of GRS 1915+105, which could be the first evidence of relaxation oscillations between the standard and slim disks.

Cluster Mergers

For many years clusters were thought to be dynamically relaxed systems evolving slowly after an initial, short-lived episode of violent relaxation. However, in a prescient paper, Gunn & Gott (1972) argued that, while the dynamical timescale for the Coma cluster, the prototype of a relaxed cluster, was comfortably less than the Hubble time, other less dense clusters had dynamical timescales comparable to or longer than the age of the Universe. Gunn and Gott concluded that The present is the epoch of cluster formation . The launch of the Einstein Observatory provided the capability to image the gravitational potential around clusters. Many papers in the 1980's, exploited the imaging of the Einstein Observatory and showed the rich and complex structure of present epoch galaxy clusters (Jones et al. 1979 Jones & Forman 1984, 1999 Forman et al. 1981 Escalera et al. 1994 Slezak et al. 1994 Salvador-Sol et al. 1993 Mohr et al. 1993, 1995). Along with the X-ray observations, optical surveys...

Computer Results

As can be seen in Fig. 1 (a), the total number of electrons Ne and ions N, in a crystal cell decrease monotonously due to their collection by the corresponding dust particle, i.e. a dusty plasma relaxation takes place. This decrease is stronger for electrons at first due to a more intensive electron flux that charges the dust particle negatively so that electron and ion fluxes are about equal. The dusty plasma relaxation is accompanied by an essential change of electron and ion velocity distribution functions that is confirmed by Fig. 2 where the mean vex relaxation start. The initial density n0 and the characteristic velocity v 0 (kTeo M) are used here for the normalization. Corresponding vy dependent functions fey and fiy are identical. As can be seen from Fig. 2, the electron velocity distribution function fe is impoverished by fast electrons during a relaxation contrary to the ion velocity distribution function , impoverished by slow ions. These effects are caused by the energy...

Isaac Newton

Throughout his life Newton appears to have been greatly interested in theological studies, and he specially devoted his attention to the subject of prophecy. He left behind him a manuscript on the prophecies of Daniel and the Apocalypse of St. John, and he also wrote various theological papers. Many other subjects had from time to time engaged his attention. He studied the laws of heat he experimented in pursuit of the dreams of the Alchymist while the philosopher who had revealed the mechanism of the heavens found occasional relaxation in trying to interpret hieroglyphics. In the last few years of his life he bore with fortitude a painful ailment, and on Monday, March 20th, 1727, he died in the eighty-fifth year of his age. On Tuesday, March 28th, he was buried in Westminster Abbey.

Elliptical galaxies

It was a mistake to think that elliptical galaxies might be close to an equilibrium state, because stellar systems have a very long memory. Most of a galaxy's stars have made fewer than 100 orbits about the center we saw in Section 3.2 that the relaxation time required to randomize their motions is far greater than the age of the Universe. If a galaxy was assembled in a triaxial shape, or with a dense central cusp, these characteristics would not yet have been erased. The variety among elliptical galaxies suggests that they originated by a number of different pathways. Present-day elliptical galaxies are 'fossils' of the earlier Universe our task is to reconstruct their birth and youthful star-forming lives from the old low-mass stars that remain.

Tectonic Activity

Extensive tectonic activity on Mercury has produced unique, large structural features. The formation of these structures has resulted, respectively, from small changes in the shape of the lithosphere induced by the sheer from tidal despinning, expansion from core formation, and contraction from core solidification (Melosh and McKinnon, 1988). The relatively extended and subdued nature of this activity resulted from Mercury's dearth of radioactive elements inducing lower internal heating and surface heat flow combined with the planet's high dayside surface temperature inducing relaxation of topographic features (Melosh and McKinnon, 1988).

Test problems

Since there are no general analytical solutions beyond the two-body problem, it is difficult to devise suitable tests for large simulation codes even in idealized form. Historically, the so-called 'IAU Comparison Problem' for N 25 Lecar, 1968 created some confusion, especially since the initial conditions gave rise to collapse and violent relaxation. The alternative approach of comparing the evolution rate with approximate methods was more successful Aarseth, Henon & Wielen, 1974 . Subsequently, the agreement with the Monte Carlo method improved further after taking into account the non-dominant terms neglected in the standard relaxation theory Henon, 1975 . A more thorough recent effort concentrated on the question of scaling to different values of N and hence bridging the gap with continuum methods Heggie et al., 1998 . The classical theory of dynamical friction has been tested by combining the gaseous model for single stars with a Monte Carlo formulation for su-perelastic binary...

Analytical Results

Typical result of the SPH simulations by Bromm et al. 2002. The figure shows the morphology of a simulated 2 x 106 Mq halo virializing at z 30 just after the formation of the first clump of mass 1400 Mq (which is likely to produce stars). The two top row panels shows the distribution of the dark matter (which is undergoing violent relaxation). The two bottom panels show the distribution of gas, which has developed a lumpy morphology and settled at the center of the potential well. Figure 5.17. Typical result of the SPH simulations by Bromm et al. 2002. The figure shows the morphology of a simulated 2 x 106 Mq halo virializing at z 30 just after the formation of the first clump of mass 1400 Mq (which is likely to produce stars). The two top row panels shows the distribution of the dark matter (which is undergoing violent relaxation). The two bottom panels show the distribution of gas, which has developed a lumpy morphology and settled at the center of the potential well.

Sample and Analysis

Our sample consists of 12 groups taken from the XMM-Newton and Chandra archives, selected to have high quality X-ray data and extended gaseous halos. All data were screened to remove periods of high background and images and spectra were extracted using standard techniques. Background spectra were created based on blank-sky data, with corrections for differences in soft flux. Annular spectra were extracted for all systems, and profiles of temperature and density were then used to estimate parameters such as gas entropy, cooling time, and total gravitational mass, under the standard assumptions of hydrostatic equilibrium and relaxation. Hardness maps were generated, and for systems with sufficient counts, adaptively binned spectral maps were used to examine the 2D temperature and abundance structure. The mapping software used 2 extracts spectra from regions centered on the pixels of the map, varying the extraction region to ensure the inclusion of a fixed number of source counts...

Ut V2TTGi16

As a field model for nonequilibrium phase transitions, we have considered a scalar whose parameters, in particular, the mass term changes signs during the phase transitions and whose quench rate is faster than the thermal relaxation rate. This model is a quantum model for the classical Landau-Ginzburg theory. It is likely that quantum decoherence of long wavelength modes by short wavelength modes may lead to the classical theory of order parameter. It is found that the topological defect density can be reduced by factors (2n + l)3 2, which is a consequence of the non-Gaussian effects and where n depends on the duration of the instability.

Idealized models

N-body simulations of core collapse with equal-mass particles were hampered by small-N limitations for a long time. However, comparison of averaged solutions for different particle numbers in the range 250-1000 Giersz & Heggie, 1994a shows excellent agreement during the pre-collapse phase when the time is scaled by the standard relaxation time factor N ln(YN). Some of these simulations employed a modified version of the code nbody 1 which included a special two-body regularization method based on time smoothing Heggie, 1972a . Likewise, anisotropic gaseous and isotropic Fokker-Planck models are in good agreement with ensemble-averaged N-body simulations both in the pre- and post-collapse phase after including an N-dependent energy generation by three-body binaries Giersz & Heggie, 1994a Giersz & Spurzem, 1994 . Moreover, the stochastic nature of the energy generation was emphasized. Statistical N-body studies also revealed self-similar solutions in the post-collapse phase in spite of...

E Profile retrieval

An alternate approach is to apply a relaxation technique similar to the method of temperature inversion discussed in Subsection 8.2.c. in this case the number of parameters describing the gas profile is chosen equal to the number of wavenumbers for which we have measurements. The radiance at each wavenumber vi is associated with a gas mole fraction qi at the atmospheric level to which the radiance is most sensitive, i.e., nearthe peak of the contribution function. A first guess, q0 (i 1, m), is introduced and used in the radiative transfer equation to calculate a set of radiances, I (vi). in order to carry out the radiance calculation it is necessary to adopt some form of interpolation between the levels for which q is initially specified. An improved solution qi1 is then obtained using the relaxation relation

Fiqi q2 qn

Convergence is usually found to be rather slow however, for many applications, it may be computationally more efficient than the linear method because it eliminates the need for evaluation of the elements of the derivative matrix. This approach, or variations on this approach, has been used extensively for determining gas composition profiles in both the Earth's atmosphere and the atmospheres of other planets. As an example, we consider the retrieval of an ammonia profile on Jupiter from measurements made by the Voyager infrared spectrometer (Kunde et al., 1982). The portion of the spectrum between 850 and 1100 cm-1 was used, as shown in Fig. 8.3.2. A modification of the relaxation method as proposed by Smith (1970) was applied to the data. The retrieved NH3 profile is shown in Fig. 8.3.3 where it is compared with the profile that would exist if ammonia were saturated at the local atmospheric temperature. The atmospheric temperature profile employed in the analysis...

Recovery phase

It has been suggested that the recovery phase is not just a simple relaxation phase. There are indications that the northward-turning of the IMF might have an influence on recovery (Rostoker, 1983). But from their magnetic field measurements at the geostationary orbit during 11 recovery phases Pulkkinen et al. (1994) concluded that the start time of the increase of Bz as well as the duration of the relaxation did not depend on the direction of the IMF z-component.


The structure of a J-shock is shown schematically in Fig. 11.1. Like a piston, a high pressure region - due to an expanding supernova, HII region, or stellar wind - is driving a shock into the surrounding medium. Now consider this in the frame of reference that is co-moving with the shock front i.e., the shock is stationary in this frame. The swept-up unshocked gas interacts through elastic collisions with the shocked gas and is decelerated that way. For neutral gas, this occurs on an elastic-collision length scale, the shock front. For low-density plasmas, the shock width will actually be further limited by plasma instabilities. In the (generally very thin) shock front, much of the (ordered) kinetic energy of motion of the gas is thus converted into (random) thermal energy through elastic collisions. In the postshock relaxation layer, the postshock gas will use this thermal energy initially for molecular dissociation and ionization processes (if possible). Downstream, the gas may...

Mind Soul Psyche

I found my philosopher forsaking mind or any other principle of order and explaining my present condition by pointing out that, as the bones are lifted at their joints by the contraction or relaxation of the muscles, I am able to bend my limbs, and this is why I am sitting here in a curved posture that is what he would say and he would have a similar explanation of my talking to you, which he would attribute to sound, and air, and hearing, and he would assign ten thousand other causes of the same sort, forgetting to mention the true cause, which is, that the Athenians have thought it fit to condemn me, and accordingly I have thought it better and more right to remain here and undergo my sentence for I am inclined to think that these muscles and bones of mine would have gone off long ago to Megara or Boeotia by the dog, they would, if they had been moved only by their own idea of what was best, and if I had not chosen the better and nobler part, instead of playing truant and running...

Interacting galaxies

Some of the earliest N-body simulations were concerned with small groups and clusters of galaxies Aarseth, 1963b, 1966a . This problem is numerically easier than point-mass dynamics and is justified because galaxies have extended mass distributions, permitting their interactions to be modelled by a softening of the Newtonian potential (cf. (2.8)). Direct integrations were performed for clusters with N 50 and 100 over a few crossing times. Since different masses were included for the first time, this was sufficient to demonstrate mass segregation and significant binaries were also noted. A subsequent investigation Aarseth, 1969 added initial rotation which gave rise to flattening, enhanced mass segregation and shorter relaxation time. Because of the general expansion of isolated systems, the rotational kinetic energy decreases. At the same time, angular momentum is transported outwards, in analogy with accretion discs. Following the development of the NBODY2 code, larger systems could...

S2y xi x

Ensembles generated by MC techniques are naturally of the constant NVT type, while MD methods naturally generate a constant NVE ensemble. Both MC and MD methods, however, may be modified to simulate other ensembles, as described in Sections 14.1.1 and 14.2.2. Of special importance is the constant NPT condition, which directly relates to most experimental conditions. The primary advantage of MD methods is that time appears explicitly, i.e. such methods are natural for simulating time-dependent properties, such as correlation functions, and for calculating properties that depend on particle velocities. Furthermore, if the relaxation time for a given process is (approximately) known, the required simulation time can be estimated beforehand (i.e. it must be at least several multiples of the relaxation time). This approach requires only a single simulation. Since the fluctuation has a longer relaxation time than the energy itself, the ensemble average in eq. (14.37) must be over a larger...

Aspects of release

Most stressing models of coronal heating invoke magnetic reconnection in one way or the other, which in essence goes back to suggestions by Gold (1964) and Parker (1979). In some of the models the reconnection process is incorporated only implicitly, for instance in the Taylor relaxation process (Section 11.5.3) (Heyvaerts and Priest, 1984) or in some of the current layer models, where current layers automatically develop into tangential discontinuities, decaying by reconnection (Parker, 1983). The reconnection process may occur in the form of small flare-like events (nanoflares), releasing energies smaller than a large flare by a factor of about 109 (Parker, 1988 Browning and Jain, 2004). Small-scale flare activity at network boundaries was invoked by Axford and McKenzie (2002). If flare mechanisms were confirmed as being relevant for coronal heating, this would bridge two historically different branches of solar physics (Vekstein and Katsukawa, 2000).


For given normal magnetic field component at the base the lowest energy configuration is the potential field. So, one might be tempted to conclude that the free energy of a stressed force-free configuration, available for release, is given by the difference between its energy and the corresponding potential field energy. This, however, is not the case, if the main relaxation process is magnetic reconnection. The reason is that the global magnetic helicity is approximately conserved (Section 11.5.3). Typically, the helicity will survive the relaxation in form of magnetic twist of large-scale magnetic flux ropes (Berger and Field, 1984 Berger, 1991).

Early Galaxy Growth

We would like to know whether bulges formed and reached their present structure quickly, or whether some galaxies built their bulges over time. Some simulations show that a thin gaseous disk can slowly construct a central bulge by scattering gas clouds out of the plane. This may apply to some spirals, especially of later types such as Sc, in which the bulge component has an exponential light profile and therefore looks more like a product of dissipation in gas rather than violent relaxation in a stellar ensemble.


The factor in parentheses on the left side of Eq. (9.2.33) is just the difference between the adiabatic and the actual lapse rate of the atmosphere. Examination of the observed temperature field indicates that the lapse rate is less than adiabatic so this factor is positive. For an upward moving parcel, the left side of Eq. (9.2.33) represents the rate at which the temperature would decrease due to adiabatic expansion, while for a downward moving parcel, this term represents the rate of increase in temperature due to adiabatic compression. These processes are sometimes called adiabatic cooling and heating. Equation (9.2.33) states that adiabatic heating or cooling due to vertical motion is balanced by the radiative relaxation of the temperature field. Thus, if we have sufficient information to calculate the radiative equilibrium temperature field and the radiative relaxation time, the temperature field retrieved from infrared measurements can be used to estimate the...

Concluding Remarks

Star clusters go through three (or four) evolutionary phases called A, B and C, each of which is dominated by either stellar mass loss or relaxation (see 8.2). In this discussion we assumed that external influences are not particularly competitive in effect, but if they are, we call them phase D. Phase D generally results in an early termination of the cluster.

Subject Index

Elastic relaxation figuring, 263, 543, 551 Elasto-optical design parameter, 185 Elasto-optics coupling, 207, 212 Electromagnetic spectrum, 27, 75 Electromagnetic theory, 27 Elliptic cylinder contour, 288 Elliptic geometry, 308 Elongated ellipsoid, 42, 384, 511 ELT, see Extremely large telescopes Enlarging monocular, 5-6, 543 Entrance pupil, 12, 36, 37, 39, 40, 465, 467, 476, 551 Stress relaxation, 342 Stress-strain linearity, 105, 112, 394, 399, 423, 553

Photophysics of PAHs


Figure 6.2 Schematic energy level diagram for a neutral PAH, illustrating the various radiative and non-radiative excitation and relaxation channels. Reproduced with permission from L.J. Allamandola, A.G.G.M. Tielens, and J.R. Barker, 1989, Ap. J. S., 71, p. 733. Figure 6.2 Schematic energy level diagram for a neutral PAH, illustrating the various radiative and non-radiative excitation and relaxation channels. Reproduced with permission from L.J. Allamandola, A.G.G.M. Tielens, and J.R. Barker, 1989, Ap. J. S., 71, p. 733. The various time scales involved in the excitation and relaxation processes are very different. Ultraviolet photon absorption in the ISM occurs on a time scale of with 0 UV(PAH) the UV absorption cross section of the PAH (approximately equal to 7 x 10-18 cm2 per carbon atom Nc ) and UV the mean photon intensity of the radiation field - here expressed in terms of the Habing field, G0. So, a typical interstellar PAH with Nc 50 absorbs a UV photon once a year in the...

Space Tourism

Tourists use discretionary funds to travel and visit destinations that remove them from the routine of everyday life. They may seek adventure, rest and relaxation, or even pampering, but in all cases they are paying for experiences. Tourism is the largest industry in the world. Because it could yield benefits for NASA, the space industry, and the public, NASA and a consortium of firms known as the Space Transportation Association are working to develop space tourism.3 Apparently, NASA has backed off from the view that space tourism is science fiction and now acknowledges its potential value as an approach to space commercialization.


As we have seen, in the MHD picture an attractive possibility for the generation of small current scales would be the formation of tangential discontinuities, where formally the current layer becomes infinitely thin (Section 3.9). It has been suggested that the shuffling of footpoints of loops or arcades by subphotospheric motions would lead to nonequilibrium and relaxation into states that contain tangential discontinuities (Parker, 1972, 1994 Low, 1987). Although the general nonequilibrium argument has been challenged (Van Ballegooijen, 1985 Zweibel and Li, 1987 Arendt and Schindler, 1988), there is ample evidence for thin current layers to form under a variety of circumstances.

John Herschel

Sir John Herschel wrote many other works besides those we have mentioned. His Treatise on Meteorology is, indeed, a standard work on this subject, and numerous articles from the same pen on miscellaneous subjects, which have been collected and reprinted, seemed as a relaxation from his severe scientific studies. Like certain other great mathematicians Herschel was also a poet, and he published a translation of the Iliad into blank verse.

B7 References

Kawamori, E., Murata, Y., Umeda, K., Hirota, D., Ogawa, T., Sumikawa, T., Iwama, T., Ishii, K., Kado, T., Itagaki, T. et al. (2005) ''Ion Kinetic Effect on Bifurcated Relaxation to a Field-Reversed Configuration in TS-4 CT Experiment'', Nuclear Fusion, Vol. 45, pp. 843-848. Stuhlinger, E. (1964) Ion Propulsion for Space Flight, McGraw-Hill, New York, Ch. 4. Taccetti, J.M., Intrator, T.P., Wurden, G.A., Zhang, S.Y., Aragonez, R., Assmus, P.N., Bass, C.M., Carey, C., deVries, S.A., Fienup, W.J. et al (2003) ''FRX-L A Field Reversed Configuration Plasma Injector for Magnetized Target Fusion'', Rev. Sci. Instruments, Vol. 74, No. 10, pp. 4314-4323. Taylor, J.B. (1976) ''Relaxation of Toroidal Discharges'', in D.E. Evans (Ed.), Pulsed High

Collective Effects

The first effect, anomalous collisions, is probably the most important macroscopic effect in a collisionless plasma. It is caused by close correlations between the particles, which replace the two-body collisions in ordinary collision-dominated systems. Binary collisions let collisional systems evolve towards relaxation and equilibrium and allow for a macroscopic description in terms of a fluid theory. In a collisionless plasma there are no binary collisions. Instead the collisions are replaced by interactions between the particles and various kinds of waves, which are responsible for relaxation processes in collisionless plasmas and ultimately justify the use of a fluid description. The immediate consequence of anomalous collisions is anomalous plasma resistivity, the appearance of finite relaxation times, and plasma diffusivity. These enter the phe-nomenological fluid equations of the plasma as transport coefficients and lead to its non-ideality.

Early influences

While studying for his degree, he had found a little diverting relaxation and the thrill of competition as a member of the college's swimming team, where he soon found himself drawn to another distraction - a young lady also from Cardiff named Valerie Mya Davies-Jones. ''She was a Physics Math major, but that wasn't a handicap '' They were married in 1957, and their first child, a son they named Gareth Roger, was born on 30 October that year.

Staying Relaxed

Staying Relaxed

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