Granular Collapse as a Percolation Transition

Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small collapsed clusters and a state dominated by a large collapsed cluster. The transition is analogous to that of a percolation transition. At the transition the number of clusters n_s of size s scales as $n_s \sim s^{-\tau}$ with $\tau \approx 2.7$.Comment: 10 pages revtex, 5 figures, accepted by Phys Rev E many changes and corrections from previous submissio

Phase Changes in an Inelastic Hard Disk System with a Heat Bath under Weak Gravity for Granular Fluidization

We performed numerical simulations on a two-dimensional inelastic hard disk system under gravity with a heat bath to study the dynamics of granular fluidization. Upon increasing the temperature of the heat bath, we found that three phases, namely, the condensed phase, locally fluidized phase, and granular turbulent phase, can be distinguished using the maximum packing fraction and the excitation ratio, or the ratio of the kinetic energy to the potential energy.It is shown that the system behavior in each phase is very different from that of an ordinary vibrating bed.Comment: 4 pages, including 5 figure

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure

Non-Newtonian Couette-Poiseuille flow of a dilute gas

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10 additional references. Published in a special issue of the journal "Kinetic and Related Models" dedicated to the memory of Carlo Cercignan

Change in Allosteric Network Affects Binding Affinities of PDZ Domains: Analysis through Perturbation Response Scanning

The allosteric mechanism plays a key role in cellular functions of several PDZ domain proteins (PDZs) and is directly linked to pharmaceutical applications; however, it is a challenge to elaborate the nature and extent of these allosteric interactions. One solution to this problem is to explore the dynamics of PDZs, which may provide insights about how intramolecular communication occurs within a single domain. Here, we develop an advancement of perturbation response scanning (PRS) that couples elastic network models with linear response theory (LRT) to predict key residues in allosteric transitions of the two most studied PDZs (PSD-95 PDZ3 domain and hPTP1E PDZ2 domain). With PRS, we first identify the residues that give the highest mean square fluctuation response upon perturbing the binding sites. Strikingly, we observe that the residues with the highest mean square fluctuation response agree with experimentally determined residues involved in allosteric transitions. Second, we construct the allosteric pathways by linking the residues giving the same directional response upon perturbation of the binding sites. The predicted intramolecular communication pathways reveal that PSD-95 and hPTP1E have different pathways through the dynamic coupling of different residue pairs. Moreover, our analysis provides a molecular understanding of experimentally observed hidden allostery of PSD-95. We show that removing the distal third alpha helix from the binding site alters the allosteric pathway and decreases the binding affinity. Overall, these results indicate that (i) dynamics plays a key role in allosteric regulations of PDZs, (ii) the local changes in the residue interactions can lead to significant changes in the dynamics of allosteric regulations, and (iii) this might be the mechanism that each PDZ uses to tailor their binding specificities regulation

VIBRATIONAL RELAXATION IN THE EXCITED ELECTRONIC STATE AND THE DEPOLARIZATION OF EMISSION

The spectral and polarization characteristics of the resonance secondary emission, such as the first order Raman scattering and hot luminescence (multiphonon Raman tail), are examined for multimode systems with a broad absorption band (i.e. strong vibronic coupling) on the example of cubic impurity centers. The transform method is generalized for nontotally symmetric modes

Theory of the vibrational structure of the Raman spectra of impure crystals

1. If the frequency of the incident light is considerably closer to the frequencies of impurity centres than to those absorbed by the pure crystal, the vibrational structure of the Raman spectra may be appreciably determined by the local dynamics of the lattice and the vibronic interaction in the impurity centre. For lack of the first order Raman spectrum of the pure crystal the matrix conditions of observing this vibrational structure are favourable in systems such as impure alkali-halide crystals. 2. It is shown that the Raman spectra would have in the Born-Oppenheimer adiabatic approximation quasi linear vibrational structure analogous to that of the absorption (luminescence) spectra : in the absence of local modes the spectrum consists of a sharp no-phonon line (the Raman analogue of the Mössbauer line) and of a considerably wider phonon band (the Raman analogue of the phonon wing of the Mössbauer line) ; a local (or pseudo-local) mode causes in addition to this aspect a series of vibrational lines. 3. For various models of the impurity centre the intensity distribution and temperature dependence of the vibrational structure are calculated. If the frequency of the incident light is close to the maximum of the impurity absorption band and the Stokes-shift is appreciable, the distribution of the intensity in a vibrational series is no longer monotonic and the maximum intensity will now belong to a vibrational line whose frequency differs from the frequency of the incident light by nω, where ω is the frequency of the local mode and n is an integer, n > 1. 4. The theoretical conclusions are compared with the experimental results of Stekhanov and Eliashberg on the Raman spectra of impure alkali-halide crystals.1. Si la fréquence de la lumière incidente est beaucoup plus voisine des fréquences d'absorption des centres d'impuretés que de celles du cristal pur, la structure vibrationnelle du spectre Raman peut être approximativement déterminée par la dynamique locale du réseau et l'interaction de ses vibrations avec les centres d'impuretés. Par suite de l'absence du spectre Raman du premier ordre pour le cristal accepteur pur, les conditions d'observation de cette structure vibrationnelle sont favorables dans les systèmes tels que les cristaux impurs d'halogénures alcalins. 2. On montre que les spectres Raman auraient, dans l'approximation adiabatique de Born-Oppenheimer, une structure vibrationnelle quasi linéaire, analogue à celle des spectres d'absorption (ou de luminescence). En l'absence de modes locaux, le spectre se compose de raies fines, sans action des phonons (analogues, pour le spectre Raman, à la raie de Mössbauer) et d'une bande due aux phonons, beaucoup plus large (analogue aux élargissements par phonons de la raie de Mössbauer). Un mode local (ou pseudo-local) ajoute à cet aspect une série de raies de vibration. 3. On calcule la répartition de l'intensité et l'action de la température sur la structure vibrationnelle pour différents modèles d'impuretés. Si la fréquence de la lumière incidente est voisine du maximum de la bande d'absorption de l'impureté et si le déplacement de Stokes est appréciable, la répartition de l'intensité dans une série vibrationnelle n'est plus monotone, et l'intensité maximale ne correspond plus à une raie de vibration dont la fréquenee diffère de nω de celle de la lumière incidente, ω étant la fréquence du mode local et n un entier, plus grand que 1. 4. On compare les conclusions théoriques avec les résultats expérimentaux de Stekhanov et Eliashberg, pour les cristaux impurs d'halogénures alcalins

Theory of the optical spectrum of Na

An analytical theory of the optical transitions of a molecule bound at the surface of a 4He droplet is developed for the case of a strong softening of the excited-state nearest neighbor dynamics. The optical bandwidth is found to be determined by the zero-point kinetic energy released at the transition. The theory is applied to the triplet-triplet optical transition in Na2 molecule, for which an asymmetric vibronic band with no pronounced zero-phonon line is predicted, in good agreement with the experiment

High-order vibrational relaxation: a nonperturbative theory

A nonperturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the positive frequency part of the time-dependent non-stationary displacement correlation function of atoms. The nonlinear integral equation for this function is derived and solved numerically. We have found that the rate exhibits a critical behavior: it sharply increases near a specific (critical) value(s) of the interaction; the corresponding dependence is characterized by the critical index , where k is the number of the created phonons