Relaxation Time Tau Research Articles

Non-homogeneous plastic deformation of amorphous metallic alloys under the action of a quasi-static mechanical load

A hypothesis is formulated and substantiated that quasi-static deformation in an amorphous metal alloy is a complex relaxation multi-stage process, which is a hierarchical sequence of interrelated structural transitions of the first order ordered in time. These nonequilibrium processes sequentially proceed at different scale space-time levels, starting from the lowest level --- a cluster of atoms of the first coordination sphere with a relaxation time taueta, then the middle level - a nanocluster of atoms of the fifth coordination sphere with a relaxation time tauφ, spatial scale of 10 nm and relaxation time tau, and tau>>tauφ>>taueta. They are accompanied by transformations of various types of potential energy of atoms (elastic, inelastic, plastic deformation, ZST) into each other. A mechanism and a model of a nonequilibrium transition from an elastic mechanical state to a state with shear transformation zones, a mechanism and a model of localized plastic deformation in an amorphous metal alloy are constructed. In the interval of non-uniqueness, in response to a locally introduced perturbation, a traveling autowave arises, which transfers the slip band from the inelastic deformation regime to the plastic deformation regime. Model parameters are estimated and important physical properties of plastic deformation are calculated. Keywords: Amorphous metal alloys, mechanical load, plastic deformation, nonequilibrium structural transition, synergetic model, kinetic equations, autowave.

Hidden transition in multiplex networks

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, P(0),=,0. Above a critical value of a control parameter, the removal of a tiny fraction Delta of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, Pi ,=,P(1). We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point Pi _c, respectively. In the limit Delta rightarrow 0 the total collapse for Pi ,>,Pi _text {c} takes a time T propto 1/(Pi -Pi _text {c}), while there is an exponential relaxation below Pi _text {c} with a relaxation time tau propto 1/[Pi _text {c}-Pi ].

Critical behavior of density-driven and shear-driven reversible\u2013irreversible transitions in cyclically sheared vortices

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, B_{mathrm {c}} and d_{mathrm {c}}, the relaxation time tau to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, tau (d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, tau (d) exhibits a power-law divergence at the same d_{mathrm {c}} with nearly the same exponent.

Pure spin photocurrent in non-centrosymmetric crystals: bulk spin photovoltaic effect

Spin current generators are critical components for spintronics-based information processing. In this work, we theoretically and computationally investigate the bulk spin photovoltaic (BSPV) effect for creating DC spin current under light illumination. The only requirement for BSPV is inversion symmetry breaking, thus it applies to a broad range of materials and can be readily integrated with existing semiconductor technologies. The BSPV effect is a cousin of the bulk photovoltaic (BPV) effect, whereby a DC charge current is generated under light. Thanks to the different selection rules on spin and charge currents, a pure spin current can be realized if the system possesses mirror symmetry or inversion-mirror symmetry. The mechanism of BSPV and the role of the electronic relaxation time tau are also elucidated. We apply our theory to several distinct materials, including monolayer transition metal dichalcogenides, anti-ferromagnetic bilayer MnBi2Te4, and the surface of topological crystalline insulator cubic SnTe.

Relaxation dynamics and crystallization study of glass-forming chiral-nematic liquid crystal S,S-2,7-bis(4-pentylphenyl)-9,9-dimethylbutyl 9H-fluorene (5P-Am*FLAm*-P5)

.The chiral nematic S,S-2,7-bis(4-pentylphenyl)-9,9-dimethylbutyl9H-fluorene (5P-Am*FLAm*-P5) liquid crystal shows a complex phase diagram strongly dependent on thermal treatment as identified by Polarizing Optical Microscopy (POM) and differential scanning calorimeter (DSC). The molecular dynamics in various thermodynamics states was studied by means of broadband dielectric spectroscopy (BDS). The vitrification of a chiral nematic phase (N*) is manifested by a Vogel-Fulcher-Tammann (VFT)-type temperature dependence of structural relaxation time (tau_{alpha}). Three dielectric relaxation processes exhibiting Arrhenius-like thermal activation were found in conformationally disordered (condis) Cr1 and Cr2 structures. The isothermal cold crystallization process of Cr2 occurs in the metastable N* phase; however, in the non-isothermal experiments, the Cr2 phase is formed in the isotropic phase obtained on heating the metastable N* phase. The findings for the isothermal process were compared with those regarding non-isothermal crystallization.Graphical abstract

The Reissner\u2013Nordstr\xf6m black hole with the fastest relaxation rate

Numerous numerical investigations of the quasinormal resonant spectra of Kerr-Newman black holes have revealed the interesting fact that the characteristic relaxation times tau ({bar{a}},{bar{Q}}) of these canonical black-hole spacetimes can be described by a two-dimensional function {{bar{tau }}}equiv tau /M which increases monotonically with increasing values of the dimensionless angular-momentum parameter {bar{a}}equiv J/M^2 and, in addition, is characterized by a non-trivial (non-monotonic) functional dependence on the dimensionless charge parameter {bar{Q}}equiv Q/M. In particular, previous numerical investigations have indicated that, within the family of spherically symmetric charged Reissner–Nordström spacetimes, the black hole with {bar{Q}}simeq 0.7 has the fastest relaxation rate. In the present paper we use analytical techniques in order to investigate this intriguing non-monotonic functional dependence of the Reissner–Nordström black-hole relaxation rates on the dimensionless physical parameter {bar{Q}}. In particular, it is proved that, in the eikonal (geometric-optics) regime, the black hole with {bar{Q}}={{sqrt{51-3sqrt{33}}}over {8}}simeq 0.73 is characterized by the fastest relaxation rate (the smallest dimensionless relaxation time {{bar{tau }}}) within the family of charged Reissner–Nordström black-hole spacetimes.

Annealing-induced magnetic moments detected by spin precession measurements in epitaxial graphene on SiC

We present results of non-local and three terminal (3T) spin precession measurements on spin injection devices fabricated on epitaxial graphene on SiC. The measurements were performed before and after an annealing step at 150 degrees Celsius for 15 minutes in vacuum. The values of spin relaxation length L_s and spin relaxation time tau_s obtained after annealing are reduced by a factor 2 and 4, respectively, compared to those before annealing. An apparent discrepancy between spin diffusion constant D_s and charge diffusion constant D_c can be resolved by investigating the temperature dependence of the g-factor, which is consistent with a model for paramagnetic magnetic moments.

Electrical conductivity of quark matter at finiteTunder external magnetic field

We investigate the electrical conductivity (sigma) of quark matter via the Kubo formula at finite temperature and zero quark density (T>0, mu=0) in the presence of an external strong magnetic field. For this purpose, we employ the dilute instanton-liquid model, taking into account its temperature modification with the trivial-holonomy caloron distribution. By doing that, the momentum and temperature dependences for the effective quark mass and model renormalization scale are carefully evaluated. From the numerical results, it turns out that sigma\approx(0.02 ~ 0.15)/fm for T=(0 ~ 400) MeV with the relaxation time tau=(0.3 ~ 0.9) fm. In addition, we also parameterize the electrical conductivity as sigma/T ~ (0.46,0.77,1.08,1.39)C_EM for tau=(0.3,0.5,0.7,0.9) fm, respectively. These results are well compatible with other theoretical estimations, including those from the lattice QCD simulations. It also turns out that the external magnetic field plays only a minor role for sigma even for the very strong one B_0 ~ m^2_pi*10 and becomes relatively effective for T\lesssim200 MeV. Moreover, we compute the soft photon emission rate from the quark-gluon plasma, using the electrical conductivity calculated.

Dynamic Heterogeneity in a Glass Forming Fluid: Susceptibility, Structure Factor, and Correlation Length

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80,000 particle system to test a new procedure to evaluate a dynamic correlation length ξ(t): we determine the ensemble independent dynamic susceptibility χ(4)(t) and use it to facilitate evaluation of ξ(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the α relaxation time τ(α), χ(4)(τ(α)), and ξ(τ(α)). We find that mode-coupling-like power laws provide a reasonable description of the data over a restricted range of volume fractions, but the power laws' exponents differ from those predicted by the inhomogeneous mode-coupling theory. We find ξ(τ(α))~ln(τ(α)) over the full range of volume fractions studied, which is consistent with an Adam-Gibbs-type relation.

Radiowave Dielectric Properties of Sodium Maleate Copolymers in Aqueous Solutions in Light of a Scaling Approach

The concentration dependence of the dielectric properties of aqueous solutions of sodium maleate copolymers with comonomers of different hydrophobicities have been investigated by means of frequency domain dielectric spectroscopy in the frequency range from 1 kHz to 2 GHz. The dielectric relaxation falling between the process at low frequencies (polarization involving the whole polymer chain) and the one at high frequencies (polarization of the bulk aqueous phase) has been analyzed in light of the scaling properties of polyelectrolyte solutions. Within this framework, the dielectric properties are governed by two characteristic lengths, the distance R(cm) between chains in the dilute regime and the correlation length xi in the semidilute regime. We find that, for both these regimes, the exponents of the scaling laws, which describe the dielectric increment Deltaepsilon and the relaxation time tau(ion) are in a reasonably good agreement with the ones experimentally observed. This analysis gives further support to the scaling approach of the dynamic behavior of polyelectrolytes, appearing very suitable to modeling our dielectric results.

Electron spin relaxation at low field

The low field ESR lineshape and the electron spin-lattice relaxation correlation function are calculated using the stochastic Liouville theory for an effective electron spin quantum number S = 1. When an axially symmetric permanent zero field splitting provides the dominant relaxation mechanism, and when it is much larger than the rotational diffusion constant, it is shown that both electron spin correlation functions S(0)S(t) (n = 0,1) are characterized by the same relaxation time tau(S) = (4D(R))(-1). This confirms the conjectures made by Schaefle and Sharp, J. Chem. Phys., 2004, 121, 5287 and by Fries and Belorizky, J. Chem. Phys., 2005, 123, 124510, based on numerical results using a different formalism. The stochastic Liouville approach also gives the paramagnetically enhanced nuclear spin relaxation time constants, T(1) and T(2), and the ESR lineshape function I(omega). In particular, the L-band (B(0) = 0.035 T) ESR spectrum of a low symmetry Ni(ii)-complex with a cylindrical ZFS tensor is shown to be detectable at sufficiently slowly reorientation of the complex. The analysis shows that the L-band spectrum becomes similar to the zero-field spectrum with a electron spin relaxation time tau(S) = (4D(R))(-1).

Transient Network Theory of Wormlike Micelles: Topological Force Accelerates Relaxation

A new transient network theory is developed to study the rheological properties of entangled wormlike micelles. The dynamic mechanical moduli are calculated on the basis of the model network in which local structure of the wormlike micelles is represented by the entangled loops. These loops interact with each other by statistical force due to the topological constraints. They are assumed to pass through each other within a finite time to release the internal stress (phantom chain-crossing model). The high frequency plateau modulus G(infinity) and the relaxation time tau as functions of the micellar concentration are calculated and compared with the experimental data on the aqueous solutions of cetyltrimethylammonium bromide (CTAB) mixed with ionic aromatic compound sodium salicylate (NaSal). It turns out that creation and annihilation of the entanglements are strongly coupled to the topological force. The rheological relaxation time decreases with the concentration of the micelles because the average radius (correlation length xi) of the entangled loops, and their contour length L decrease with the CTAB concentration. Hence, the topological force is amplified by the increase in the concentration and, as a result, accelerates the stress relaxation by chain-crossing.

Density scaling in viscous liquids: From relaxation times to four-point susceptibilities

We present numerical calculations of a four-point dynamic susceptibility, chi(4)(t), for the Kob-Andersen Lennard-Jones mixture as a function of temperature T and density rho. Over a relevant range of T and rho, the full t-dependence of chi(4)(t) and thus the maximum in chi(4)(t), which is proportional to the dynamic correlation volume, are invariant for state points for which the scaling variable rho(gamma)/T is constant. The value of the material constant gamma is the same as that which superposes the relaxation time tau of the system versus rho(gamma)/T. Thus, the dynamic correlation volume is a unique function of tau for any thermodynamic condition in the regime where density scaling holds. Finally, we examine the conditions under which the density scaling properties are related to the existence of strong correlations between pressure and energy fluctuations.

Shear Viscosity Coefficient and Relaxation Time of Causal Dissipative Hydrodynamics in QCD

The shear viscosity coefficient and the corresponding relaxation time for causal dissipative hydrodynamics are calculated based on the microscopic formula proposed in T. Koide and T. Kodama [Phys. Rev. E 78, 051107 (2008)10.1103/PhysRevE.78.051107]. Here, the exact formula is transformed into a more compact form and applied to evaluate these transport coefficients in the chiral perturbation theory and perturbative QCD. It is shown that in the leading order calculation, the causal shear viscosity coefficient eta reduces to that of the ordinary Green-Kubo-Nakano formula, and the relaxation time tau(pi) is related to eta and pressure P by a simple relationship, tau(pi)=eta/P.

Single chain dynamics in polymer networks: A Monte Carlo study

We investigated the dynamics of single chains diffusing in cross-linked polymer networks using the three-dimensional bond fluctuation method. We considered single chain dynamics in dry polymer networks, at monomer density of 0.51, and similarly, in networks swollen up to the maximum degree of swelling. In order to compare time scales at different degrees of network swelling we calculated the single monomer relaxation time tau(0), which showed a strong decrease with swelling. The scaling laws of terminal relaxation times tau(d) and the diffusion coefficients D as function of renormalized chain length covered both the Rouse and the entangled regime. We found that the entanglement length N(e) as function of monomer density of the network has similar values to those calculated for polymer melts, at the same concentration. The effect of fixed topological constraints in polymer networks on the concentration dependence of the entanglement length is discussed.

Dynamics of a protein and its surrounding environment: A quasielastic neutron scattering study of myoglobin in water and glycerol mixtures

In this quasielastic neutron scattering (QENS) study we have investigated the relation between protein and solvent dynamics. Myoglobin in different water:glycerol mixtures has been studied in the temperature range of 260-320 K. In order to distinguish between solvent and protein dynamics we have measured protonated as well as partly deuterated samples. As commonly observed for bulk as well as for confined water, the dynamics of the surrounding solvent is well described by a jump diffusion model. The intermediate scattering function I(Q,t) from the protein (partly deuterated samples) was analyzed by fitting a single Kohlrausch-Williams-Watts (KWW) stretched exponential function to the data. However, due to the limited experimental time window, two different curve fitting approaches were used. The first one was performed with the assumption that I(Q,t) decays to zero at long times, i.e., it was assumed that all protein relaxations that are observed on the experimental time scale, as well as would be observed on longer time scales, can be described by a single KWW function. In the second approach we instead assumed that both the protein relaxation time tau(p) and the stretching parameter beta(KWW) were Q-independent, i.e., we assumed that the protein dynamics is dominated by more local motions. Advantages and disadvantages of both approaches are discussed. The first approach appears to work best at higher Q-values, indicating a power law relation of the Q-dependent protein dynamics for all samples and temperatures, whereas the second approach seems to work at lower Q-values, where the expected confined diffusion of hydrogen atoms in the protein gives the assumed Q-independent relaxation time. Independent of the chosen approach we find a significant correlation between the average relaxation time of the protein and the diffusion constant (or in this case the related relaxation time) of the solvent. However, the correlation is not perfect since the average relaxation time of the protein is more strongly dependent on the total amount of solvent than the diffusion constant of the solvent itself. Thus, the average relaxation time of the protein decreases not only with increasing solvent mobility, but also with increasing solvent content.

Simulating dynamic crossover behavior of semiflexible linear polymers in solution and in the melt

We present a molecular dynamics study of the dynamic scaling behavior of linear polymers in solution and in the melt when their character changes from fully flexible to semiflexible. The stiffness of the chains is determined by a bending potential. It is shown that the relaxation times tau(p) characterizing the internal dynamics of the polymer chains as well as the mean square mode amplitudes <chi(p)(2)> exhibit a clear crossover from Rouse to bending modes with increasing mode number p. For small mode numbers p the well-known p(-2) Rouse behavior is observed, whereas large mode numbers exhibit the p(-4) scaling, typical of the bending modes of semiflexible chains. We study the extension and the onset of the region where the crossover from p(-2) to p(-4) behavior occurs. With increasing stiffness of the chains we observe a shift of the crossover domain to smaller p-values. We also investigate the effect of chain stiffness on the monomer dynamics, based on their mean square displacements. Finally, we compare our results to previous simulations, where the scaling behavior of semiflexible chains was studied and which were restricted to a smaller range of persistence lengths l(p) and p values.

Structure, Dynamic Properties, and Phase Transitions of Tethered Membranes

A coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination, embedded in three-dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5 < or =L< or = 30. We find that the membrane undergoes several folding transitions from a high-temperature flat phase to multiple-folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues lambda(2) (max)> or =lambda(2) (med)> or =lambda(2) (min) of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high temperature flat phase, the radius of gyration R(g) grows with the linear size of the membrane L as R(g) proportional, variant L(nu), where the exponent nu approximately 1.0. The eigenvalues of the inertia tensor scale as lambda(max) proportional, variant lambda(med) proportional, variant L(nu) and lambda(min) proportional variant L(nu min) whereby the roughness exponent nu(min) approximately 0.7. We also find that the Rouse relaxation time tau(R) of a self-avoiding membrane scales as tau(R) proportional, variant L(2nu+2), in good agreement with the theoretical predictions.

Quasielastic neutron scattering investigation of motion of water molecules in n-propyl alcohol-water mixture

The dynamics of water molecules in the n-propyl alcohol-water mixtures is investigated by using quasielastic neutron scattering measurements. The dynamic structure factor S(Q,E) obtained from incoherent scattering of hydrogen atoms of water is fitted with jump diffusion and relaxing cage models. The diffusion constant obtained from the relaxing cage model, which gives better fitting with S(Q,E), shows better agreement to the experimental value than that of jump diffusion model. The dependence of translational relaxation time tau(T)(Q) and stretched exponent beta(T)(Q) on the fraction of hydrophobic hydrating water molecules in the solution is discussed.

Nondriven polymer translocation through a nanopore: Computational evidence that the escape and relaxation processes are coupled

Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that the characteristic relaxation time of the chain is small enough compared to the translocation time that nonequilibrium molecular conformations can be ignored. In this paper, we use molecular dynamics simulations to directly test this hypothesis by looking at the escape time of unbiased polymer chains starting with different initial conditions. We find that the translocation process is not quite in equilibrium for the systems studied, even though the translocation time tau is about 10 times larger than the relaxation time tau{r}. Our most striking result is the observation that the last half of the chain escapes in less than approximately 12% of the total escape time, which implies that there is a large acceleration of the chain at the end of its escape from the channel.