Arbitrary Relaxation Research Articles

Arbitrary relaxation rate under non-Hermitian matrix iterations

We study the exponential relaxation of observables propagated with a non-Hermitian transfer matrix, an example being out-of-time-ordered correlations (OTOC) in brick-wall (BW) random quantum circuits. Until a time that scales as the system size, the exponential decay of observables is not usually determined by the second largest eigenvalue of the transfer matrix, as one can naively expect, but it is, in general, slower—this slower decay rate was dubbed “phantom eigenvalue.” Generally, this slower decay is given by the largest value in the pseudospectrum of the transfer matrix; however, we show that the decay rate can be an arbitrary value between the second largest eigenvalue and the largest value in the pseudospectrum. This arbitrary decay can be observed, for example, in the propagation of OTOC in periodic boundary conditions BW circuits. To explore this phenomenon, we study a matrix iteration made from a simple tridiagonal Toeplitz matrix. This setting can be used to propagate OTOC in random circuits with open boundary conditions and to describe a one-dimensional biased random walk with dissipation at the edges. Published by the American Physical Society 2024

Phase separation and ripening in a viscoelastic gel

The process of phase separation in elastic solids and viscous fluids is of fundamental importance to the stability and function of soft materials. We explore the dynamics of phase separation and domain growth in a viscoelastic material such as a polymer gel. Using analytical theory and Monte Carlo simulations, we report a domain growth regime in which the domain size increases algebraically with a ripening exponent [Formula: see text] that depends on the viscoelastic properties of the material. For a prototypical Maxwell material, we obtain [Formula: see text], which is markedly different from the well-known Ostwald ripening process with [Formula: see text]. We generalize our theory to systems with arbitrary power-law relaxation behavior and discuss our findings in the context of the long-term stability of materials as well as recent experimental results on phase separation in cross-linked networks and cytoskeleton.

Nontrivial solutions for arbitrary order discrete relaxation equations with periodic boundary conditions

Nontrivial solutions for arbitrary order discrete relaxation equations with periodic boundary conditions

The gender features of the development of the ability to relax muscles at random in visually impaired pupils of the basic school

The article considers the influence of the level of development of the ability to arbitrary muscle relaxation on a person's physical condition. The indicators of the development of voluntary muscle relaxation have been studied in visually impaired pupils of the basic school, which were determined by the test results, based on a visual assessment of the quality of the student's performance of relaxed, whip-shaped waves legs. A comparative analysis of the studied indicators in the specified contingent depending on sex and age is given. The age dynamics of indicators of development of the ability to arbitrarily relax muscles in boys and girls aged 10-16 by gender is considered.
 The study was conducted on the basis of the municipal institution «Kharkiv special boarding school I–III degrees № 12» Kharkiv Regional Council for children with visual impairments, which involved pupils of 5–10 grades with visual analyzer disorders, aged 10–16 years. From the principal, pediatrician, ophthalmologist and parents of the pupils permission was obtained to conduct the study. To achieve the goal of the study, the following methods were used: theoretical analysis and generalization of scientific and methodological literature, pedagogical testing and statistical methods of processing results.
 It was found, that the best indicators of voluntary muscle relaxation were found in schoolboys of 7th and in schoolgirls of 5th grades. Note, that the girls the results of implementation of whip-shaped waves legs , for the most part, better than the boys. In the dynamics of indicators of the development of the ability to arbitrarily relax muscles in visually impaired middle school students with age, there are wave-like changes.

Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer

We describe compressible two-phase flows by a single-velocity six-equation flow model, which is composed of the phasic mass and total energy equations, one volume fraction equation, and the mixture momentum equation. The model contains relaxation source terms accounting for volume, heat and mass transfer. The equations are numerically solved via a fractional step algorithm, where we alternate between the solution of the homogeneous hyperbolic portion of the system via a HLLC-type wave propagation scheme, and the solution of a sequence of three systems of ordinary differential equations for the relaxation source terms driving the flow toward mechanical, thermal and chemical equilibrium. In the literature often numerical relaxation procedures are based on simplifying assumptions, namely simple equations of state, such as the stiffened gas one, and instantaneous relaxation processes. These simplifications of the flow physics might be inadequate for the description of the thermodynamical processes involved in various flow problems. In the present work we introduce new numerical relaxation techniques with two significant properties: the capability to describe heat and mass transfer processes of arbitrary relaxation time, and the applicability to a general equation of state. We show the effectiveness of the proposed methods by presenting several numerical experiments.

Spectral method for time-strain separable integral constitutive models in oscillatory shear

The time-strain separable Kaye–Bernstein–Kearsley–Zappas model (tssKBKZM) is a popular integral constitutive equation that is used to model the nonlinear response of time-strain separable materials using only their linear viscoelastic properties and damping function. In oscillatory shear, numerical evaluation of tssKBKZM is complicated by the infinite domain of integration, and the oscillatory nature of the integrand. To avoid these problems, a spectrally accurate method is proposed. It approximates the oscillatory portion of the integrand using a discrete Fourier series, which enables analytical evaluation of the resulting integrals for the Maxwell model. The spectral method is generalized for arbitrary discrete and continuous relaxation spectra. Upper bounds for quadrature error, which can often be driven to machine precision, are presented. The Doi–Edwards model with independent-alignment approximation (DE-IA) is a special case of tssKBKZM; for DE-IA, the spectral method is compared with trapezoidal rule to highlight its accuracy and efficiency. The superiority of the proposed method is particularly evident at large strain amplitude and frequency. For continuous relaxation spectra, the spectral method transforms the double integral corresponding to the tssKBKZM to a single integral. Solutions computed to a specified level of accuracy using standard numerical libraries show that the spectral method is typically two to three orders of magnitude faster. Extensions to fractional rheological models, materials with nonzero equilibrium modulus, stretched exponential models, etc., are also discussed.

Creep tide model for the three-body problem

We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into account. Based on the creep tide theory, we present a set of differential equations that describes the rotational evolution of each body, in a formalism that is easily extensible to the N tidally interacting body problem. We apply our model to the case of a circumbinary planet and use a Kepler-38 like binary system as a working example. We find that, in this low planetary eccentricity case, the most likely final stationary rotation state is the 1:1 spin–orbit resonance, considering an arbitrary planetary viscosity inside the estimated range for the Solar System planets. The timescales for reaching the equilibrium state are expected to be approximately millions of years for stiff bodies but can be longer than the age of the system for planets with a large gaseous component. We derive analytical expressions for the mean rotational stationary state, based on high-order power series of the ratio of the semimajor axes a1∕a2 and low-order expansions of the eccentricities. These are found to very accurately reproduce the mean behaviour of the low-eccentric numerical integrations for arbitrary planetary relaxation factors, and up to a1∕a2 ~ 0.4. Our analytical model is used to predict the stationary rotation of the Kepler circumbinary planets and we find that most of them are probably rotating in a subsynchronous state, although the synchrony shift is much less important than our previous estimations. We present a comparison of our results with those obtained with the Constant Time Lag and find that, as opposed to the assumptions in our previous works, the cross torques have a non-negligible net secular contribution, and must be taken into account when computing the tides over each body in an N-extended-body system from an arbitrary reference frame. These torques are naturally taken into account in the creep theory. In addition to this, the latter formalism considers more realistic rheology that proved to reduce to the Constant Time Lag model in the gaseous limit and also allows several additional relevant physical phenomena to be studied.

Spectroscopic analysis in molecular simulations with discretized Wiener-Khinchin theorem for Fourier-Laplace transformation.

The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to obtain the single-side Fourier transforms of arbitrary time-domain relaxation functions (or autocorrelation functions). Moreover, by combining an on-the-fly algorithm with the WKT-FLT, the numerical calculations of various complex spectroscopic data in a wide frequency range become significantly more efficient. However, the discretized WKT-FLT equation, obtained simply by replacing the integrations with the discrete summations, always produces two artifacts in the frequency-domain relaxation function. In addition, the artifacts become more apparent in the frequency-domain response function converted from the relaxation function. We find the sources of these artifacts that are associated with the discretization of the WKT-FLT equation. Taking these sources into account, we derive discretized WKT-FLT equations designated for both the frequency-domain relaxation and response functions with the artifacts removed. The use of the discretized WKT-FLT equations with the on-the-fly algorithm is illustrated by a flow chart. We also give application examples for the wave-vector-dependent dynamic susceptibility in an isotropic amorphous polyethylene and the frequency-domain response functions of the orientation vectors in an n-alkane crystal.

Общие свойства показателя скоростной чувствительности диаграмм деформирования, порождаемых линейной теорией вязкоупругости и существование максимума у его зависимости от скорости

Анализируется скоростная чувствительность семейства диаграмм деформирования, порождаемых физически линейным определяющим соотношением вязкоупругости Больцмана-Вольтерры с произвольной функцией релаксации в одноосных испытаниях с постоянными скоростями деформации. Выведено общее выражение для показателя скоростной чувствительности (скоростного упрочнения) и аналитически исследованы его общие качественные свойства: зависимость от деформации, скорости деформации и характеристик функции релаксации, диапазон значений, интервалы монотонности и существование точек экстремума, предельные значения при стремлении скорости деформации к нулю или бесконечности, способы определения по диаграммам деформирования или по кривым релаксации. Установлено, что (в рамках линейной теории вязкоупругости) этот показатель зависит не от двух независимых аргументов (деформации и скорости деформации), а только от их отношения, что он выражается через отношение касательного модуля к секущему и может быть вычислен по одной диаграмме деформирования с произвольной скоростью деформации, и что по заданной (или измеренной в испытаниях) функции скоростной чувствительности можно однозначно восстановить функцию релаксации. Доказано, что значения показателя скоростной чувствительности всегда лежат в интервале от нуля до единицы (т.е. линейное определяющее соотношение описывает только псевдопластические среды и не может описывать дилатантные) и могут быть сколь угодно близки к единице (верхней границе для псевдопластических сред), что как функция скорости он не только может монотонно возрастать или убывать, но может иметь точки экстремума, в частности точку максимума (при малообременительных ограничениях на функцию релаксации). Тем самым обнаружена неожиданная способность линейной теории вязкоупругости не только порождать семейство диаграмм деформирования с выраженными участками течения при практически постоянном напряжении, но и качественно описывать «сигмоидальную» форму зависимости напряжения от скорости деформации (в логарифмических осях) и очень высокую скоростную чувствительность, характерные для режима сверхпластического деформирования материалов. Установленные свойства показателя скоростной чувствительности и его характерные особенности проиллюстрированы на примерах классических регулярных, сингулярных и фрактальных моделей вязкоупругости (Максвелла, Фойгта, Кельвина, Зенера, Бюргерса, Скотт-Блэра) и их параллельных соединений.

Застосування методики проведення релаксації у процесі підготовки вчителів фізичного виховання

The article describes the method of relaxation. The ability to relax can prevent or compensate for the damage to the body that causes it to feel nervous. An important condition for mastering the methods of psychophysical training is the ability to regulate the process of respiration, the muscular state and the state of the psyche. Under the influence of relaxation, the flow of impulses from muscles, connective tissue and joints in the central nervous system decreases. As a result, the transition from muscle tension to relaxation and again to stress will contribute to the peculiar gymnastics of nerve centers. An arbitrary relaxation of the muscles (relaxation) is based on the ability of a person mentally with a figurative idea to disconnect the muscles from pulses coming from the motor centers of the brain. General relaxation of muscles is recommended to everyone. Assimilating muscle relaxation, it is necessary to avoid the usual spontaneous movements in everyday life - twitching shoulders, wrinkling forehead, strong gestures. Avoiding spontaneous movements, we save nervous energy. Face expression, regardless of the situation, should always be relaxed, friendly. When the skills of general relaxation of the muscles of the body will be learned, you should learn to call on memory the feeling of warming your arms and legs. Conscious control of breathing and muscle tone leads to the assimilation of neuromotor regulation. That is why you need to master these exercises separately and in combination with proper breathing. In our method, we use several techniques that help you master the technique of relaxation. Here are the tricks: the method of simulation; method of comfortable position lying; method of tension and relaxation of muscles; breathing “in a circle”; verbal method. These techniques can be used alone or in combination, depending on individual characteristics, which facilitate the rapid assimilation of muscle relaxation techniques. Exercise for relaxation is especially useful for those muscles that are in constant stress in the working position. As a result of the research it was found that deep relaxation of the muscular system gives the person a sense of self-control and rest, provides a quick recovery of strength, and for this purpose it is necessary to learn to feel the state of his muscular system and to manage it with the help of several techniques that help assimilate the technique of relaxation.

Two-Sided Estimates for the Relaxation Function of the Linear Theory of Heredity via the Relaxation Curves during the Ramp-Deformation and the Methodology of Identification

The general properties of the relaxation curves with the initial stage of deformation and their dependence on the duration of the initial stage of deformation and the properties of the relaxation function are analytically studied. These curves are induced by the constitutive equation of viscoelasticity with an arbitrary relaxation. New accurate two-sided estimates for the relaxation curves and their absolute and relative deviations from the relaxation curves for instantaneous deformation are derived. The uniform convergence of the set of relaxation curves when the duration of the initial stage tends to zero is proved. Effective universal two-sided estimates for the relaxation function (at any time instant) are obtained via the relaxation curves of the material during ramp-deformation. On their basis, simple and effective formulas for determining the relaxation function from the relaxation curves for ramp deformation obtained in the material tests have been proposed. The error estimations of these approximations are given. The uniform convergence of the set of approximations to the relaxation function when the duration of the initial stage tends to zero is proved. The higher accuracy of the estimates found and the proposed approximation in comparison with the known related approaches to the determination of the RF (relaxation function) is established. The results of the analysis are useful for clarifying the many of the possibilities of the linear theory, the domain and indicators of its (non)applicability (and also of a number of its generalizing nonlinear constitutive equations of viscoelasticity, for example, proposed by Rabotnov,Ilyushin, Pobedrya, etc.) to improve the methods of selection, identification and adjustment of linear models. In particular, they are useful for obtaining reliable estimates of the lower bound for the observation window of the relaxation function from the experimental relaxation curve of the material in terms of the initial stage duration to clarify the “ten-times rule” and expand the observation window to the region of small time values.

Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction

This paper presents the stability, convergence and optimization characteristics of interface treatments for steady conjugate heat transfer problems. The Dirichlet-Robin and Neumann-Robin procedures are presented in detail and compared on the basis of the Godunov-Ryabenkii normal mode analysis theory applied to a canonical aero-thermal coupling prototype. Two fundamental parameters are introduced, a “numerical” Biot number that controls the stability process and an optimal coupling coefficient that ensures unconditional stability. This coefficient is derived from a transition of the amplification factor. A comparative study of these two treatments is made in order to implement numerical schemes based on adaptive and local coupling coefficients, with no arbitrary relaxation parameters, and with no assumptions on the temporal advancement of the fluid domain. The coupled numerical test case illustrates that the optimal Dirichlet-Robin interface conditions provide effective and oscillation-free solutions for low and moderate fluid-structure interactions. Moreover, the computation time is slightly shorter than the time required for a CFD computation only. However, for higher fluid-structure interactions, a Neumann interface condition on the fluid side presents good numerical properties so that no relaxation coefficients are required.

ПСИХОЛОГІЧНІ ОСОБЛИВОСТІ РОЗВИТКУ САНОГЕННОГО ПОТЕНЦІАЛУ ЯК ЧИННИКА ПРОФЕСІЙНОЇ СТІЙКОСТІ ОСОБИСТОСТІ МАЙБУТНЬОГО ПСИХОЛОГА

The scientific article is devoted to the problem of determining the characteristics of the sanogenic potential as a factor in the professional stability of the personality of a future psychologist-practitioner. The urgency of the problem is determined by the conditions for optimizing the personality-professional development of future practicing psychologists, personal maturity, the integration of self-concept and the development of a person’s sanogenic potential as aspects of professional stability, effective professional self-realization and the factors of preserving a person’s mental health. In order to develop the sanogenic personality potential of future psychologists, a training program "Development of the sanogenic personality potential: stress resistance and time management" was developed on the basis of a stress model. The purpose of the program is to increase the overall level of sanogenic potential of the individual. Particular attention is paid to forming a positive image of a stressful situation, learning to cognitively analyze the situation, predicting behavior as appropriate, updating the skills of arbitrary relaxation and developing experience in applying techniques and formulas for constructive response in solving professional problems. The program is created in accordance with the principles of the concept of accelerated learning (Accelerated Learning Theory) and uses all the latest developments in the field of adult learning methodology. Analyzing the results, we can say that the psycho-correction program has helped to increase the level of emotional stability and sanogenic potential of future psychologists. Students have decreased levels of situational and personal anxiety, decreased levels of feelings of insecurity, anxiety, inferiority, anxiety about work, sensitivity to failure (reflects the scale of "emotional"), increased the level of flexibility of thinking and behavior, ability to change shows the plasticity scale).

The Global Kondaurov Double Porosity Model

In this paper we derive a non-equilibrium matrix imbibition equation for the homogenized Kondaurov double porosity model which is valid for arbitrary relaxation times. This equation involves the real saturation and Kondaurov's non-equilibrium parameter, i.e., the principal unknowns of the model. The numerical simulation of the obtained result is also presented.

General properties of relaxation curves in the case of the initial stage of strain with a constant rate in the linear heredity theory

Qualitative properties of relaxation curves are analytically studied in the case of linear-time strain at the initial stage. These curves are induced by an integral constitutive relation of viscoelasticity with an arbitrary relaxation function. Among these properties are the intervals of monotonicity and convexity, jumps, breaks, the asymptotics of curves, their dependence on the parameters of the initial stage of strain and on the properties of a relaxation function, the convergence type of a family of relaxation curves when the duration of the initial stage tends to zero, etc.

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method.

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S2(ππ*)-S1(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system-bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system-bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system-bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S2) is very efficiently quenched by the system-bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode-mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system-bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system-bath coupling as well as the field-matter coupling.

Conductance of a single electron transistor with a retarded dielectric layer in the gate capacitor

We study conductance of a single electron transistor (SET) with a ferroelectric (or dielectric) layer placed in the gate capacitor. We assume that ferroelectric (FE) has a retarded response with arbitrary relaxation time. We show that in the case of "fast" but still retarded response of the FE (dielectric) layer an additional contribution to the Coulomb blockade effect appears leading to the suppression of the SET conductance. We take into account fluctuations of the FE (dielectric) polarization using Monte-Carlo simulations. For "fast" FE these fluctuations partially suppress the additional Coulomb blockade effect. Using Monte-Carlo simulations we study the transition from "fast" to "slow" FE. For high temperatures the peak value of the SET conductance is almost independent of the FE relaxation time. For temperatures close to the FE Curie temperature the conductance peak value non-monotonically depends on the FE relaxation time. A maximum appears when the FE relaxation time is of the order of the SET discharging time. Below the Curie point the conductance peak value decreases with increasing the FE relaxation time. The conductance shows the hysteresis behavior for any FE relaxation time at temperatures below the FE transition point. We show that conductance hysteresis is robust against FE internal fluctuations.

Rapid measurement of multidimensional 1H solid-state NMR spectra at ultra-fast MAS frequencies

A novel method to realize rapid repetition of 1H NMR experiments at ultra-fast MAS frequencies is demonstrated. The ultra-fast MAS at 110kHz slows the 1H–1H spin diffusion, leading to variations of 1H T1 relaxation times from atom to atom within a molecule. The different relaxation behavior is averaged by applying 1H–1H recoupling during relaxation delay even at ultra-fast MAS, reducing the optimal relaxation delay to maximize the signal to noise ratio. The way to determine optimal relaxation delay for arbitrary relaxation curve is shown. The reduction of optimal relaxation delay by radio-frequency driven recoupling (RFDR) was demonstrated on powder samples of glycine and ethenzamide with one and multi-dimensional NMR measurements.

Determination of critical current density from arbitrary flux relaxation process

The current-carrying ability of a type-II superconductor is generally represented by its critical current density. This can be determined by measuring a flux relaxation process starting with a testing current density that is greater than or equal to the critical value. Here we show that a flux relaxation process starting with an intermediate current density can be converted into a process starting with the critical current density by introducing a virtual time interval. Therefore, one may calculate the critical current density from the flux relaxation process starting with a current density below the critical value. The exact solutions of the time dependence of current density in the flux relaxation process were also discussed.

On the Exact Solution of a Generalized Polya Process

There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non‐stationary type master equation approach. For a transition‐rate with an arbitrary time‐dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time‐dependent relaxation functions reflecting memory in the systems.