We study the stochastic resonance (SR) of a flexible polymer chain crossing over a piecewise linear bistable potential. The dependence of signal to noise ratio $SNR$ on noise intensity $D$, coupling constant $k$ and polymer length $N$ is studied via two state approximation. We find that the response of signal to the background noise strength is significant at optimum values of $D_{opt}$, $k_{opt}$ and $N_{opt}$ which suggests novel means of manipulating proteins or vesicles. Furthermore, the thermally activated barrier crossing rate $r_{k}$ for the flexible polymer chain is studied. We find that the crossing rate $r_{k}$ exhibits an optimal value at an optimal coupling constant $k_{opt}$; $k_{opt}$ decreases with $N$. As the chain length $N$ increases, the escape rate for the center of mass $r_{k}$ monotonously decreases. On the other hand, the crossing rate for the portion of polymer segment $r_s$ increases and saturates to a constant rate as $N$ steps up.
The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential landscape, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level.
We investigate interface motion in disordered ferromagnets by means of Monte Carlo simulations. For small temperatures and driving fields a so-called creep regime is found and the interface velocity obeys an Arrhenius law. We analyze the corresponding energy barrier as well as the field and temperature dependence of the prefactor.
We study the effect of a non-Gaussian noise on interstate switching activated primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change the switching rate. The effect is determined by all moments of the noise distribution. The explicit analytical results are compared with the results of simulations for an overdamped system driven by white Gaussian noise and a Poisson noise. Switching induced by a purely Poisson noise is also discussed.
A random fuse network, or equivalently a two-dimensional spring network with quenched disorder, is subjected to a constant load and thermal noise, and studied by means of numerical simulations. Rupture is thermally activated and the lifetime follows an Arrhenius law where the energy barrier is reduced by disorder. Due to the non-homogeneous distribution of forces from the stress concentration at microcrack tips, spatial correlations between rupture events appear, but they do not affect the energy barrier's dependence on the disorder; they affect only the coupling between the disorder and the a…
The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape …
We explore the dependence of the thermally activated barrier crossing rate on various model parameters for a dimer that undergoes a Brownian motion on a piecewise linear bistable potential employing the method of adiabatic elimination of fast variable. By introducing a different model system and approaches than the previous works \cite{c4,c5}, not only we recapture the previous results but we further show that systematic elimination of the fast changing variable leads to an effective Kramers type potential. It is shown that for rigid dimer, the escape rate $R$ monotonously decreases with $k$. …
Thermally activated magnetization decay is studied in ensembles of clusters of interacting dipolar moments by applying the master-equation formalism, as a model of thermal relaxation in systems of interacting single-domain ferromagnetic particles. Solving the associated master-equation reveals a breakdown of the energy barrier picture depending on the geometrical symmetry of structures. Deviations are most pronounced for reduced symmetry and result in a strong interaction dependence of relaxation rates on the memory of system initialization. A simple two-state system description of an ensemble…
We analyze the evaporation and condensation of spherical and cylindrical HI clouds of the cold neutral medium surrounded by the warm neutral medium. Because the interstellar medium including those two phases is well described as a thermally bistable fluid, it is useful to apply pattern formation theories to the dynamics of the interface between the two phases. Assuming isobaric evolution of fluids and a simple cubic form of the heat-loss function, we show the curvature effects of the interface. We find that approximate solutions for spherical clouds are in good agreement with numerically obtai…
We study the fluctuation-activated transition process in a system of two coupled bistable oscillators, in which each oscillator is driven by one constant force and an independent Gaussian white noise. The transition pathway has been identified and the transition rate has been computed as the coupling strength $μ$ and the mismatch $σ$ in the force constants are varied. For identical oscillators ($σ=0$), the transition undergoes a change from a two-step process with two candidate pathways to a one-step process with also two candidate pathways to a one-step process with a single pathway as $μ$ is…
Impact phenomena of small clusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions can exceed unity when the colliding speed is smaller than the thermal velocity of one ``atom'' of the clusters. The averaged behavior can be understood by the quasi-static theory of impact phenomena. It is also confirmed that our result is governed by the fluctuation theorem.
Sorting the integers 1 through $N$ into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally-activated pairwise exchanges of neighboring list elements, we find sorting can display many features of a glass, even for lists as small as $N = 5$. This includes memory and rejuvenation effects during aging --- two hallmarks of glassy dynamics that have been difficult to reproduce in standard glass simulations.
Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxia…
Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions has a peak at a colliding speed due to the competition between the cohesive interaction and the repulsive interaction of colliding clusters. Some aspects of the collisions can be understood by the theory by Brilliantov {\it et al.} (Phys. Rev. E {\bf 76}, 051302 (2007)), but many new aspects are found from the simulation. In particular, we find that there ar…
Constriction-based Josephson weak-links display a thermal bi-stability between two states exhibiting zero and finite voltages. This manifests in experiments either as hysteresis in weak-links current voltage characteristics or as random telegraphic signal in voltage. In the latter case, a noise-driven amplification of a sinusoidal excitation of the device is observed, at frequencies matching the characteristic switching frequency in telegraphic signal, a phenomenon known as stochastic resonance. The observed behavior is understood using a two-state model of stochastic resonance and is exploite…
We consider the thermally activated fragmentation of a homopolymer chain. In our simple model the dynamics of the intact chain is a Rouse one until a bond breaks and bond breakdown is considered as a first passage problem over a barrier to an absorbing boundary. Using the framework of the Wilemski-Fixman approximation we calculate activation times of individual bonds for free and grafted chains. We show that these times crucially depend on the length of the chain and the location of the bond yielding a minimum at the free chain ends. Theoretical findings are qualitatively confirmed by Brownian…
The lifetime of a porous media, submitted to a constant subcritical stress, is studied by means of a numerical model. This model is based on a spring network where the porosity is represented by missing springs. The dynamics is produced adding thermal fluctuations in spring forces. The lifetime predicted by the models are compared to experimental data of delayed fracture of porous media submitted to three-point flexion fracture experiments.
We present a study of static and frequency-dependent diffusion with anisotropic thermally activated transition rates in a two-dimensional bond percolation system. The approach accounts for temperature effects on diffusion coefficients in disordered anisotropic systems. Static diffusion shows an Arrhenius behavior for low temperatures with an activation energy given by the highest energy barrier of the system. From the frequency-dependent diffusion coefficients we calculate a characteristic frequency $ω_{c}\sim 1/t_{c}$, related to the time $t_c$ needed to overcome a characteristic barrier. We …
We demonstrate that a Peierls dimerization can occur in ferromagnetic spin chains activated by thermal fluctuations. The dimer order parameter and entanglement measures are studied as functions of the modulation of the magnetic exchange interaction and temperature, using a spin-wave theory and the density-matrix renormalization group. We discuss the case where a periodic modulation is caused by spin-phonon coupling and the case where electronic states effectively induce such a modulation. The importance of the latter for a number of transition metal oxides is highlighted.
We study numerically the out-of-equilibrium dynamics of interfaces at finite temperatures when driven well below the zero-temperature depinning threshold. We go further than previous analysis by including the most relevant non-equilibrium correction to the elastic Hamiltonian. We find that the relaxation dynamics towards the steady-state shows glassy behavior, aging and violation of the fluctuation-dissipation theorem. The interface roughness exponent alpha approx 0.7 is found to be robust to temperature changes. We also study the instantaneous velocity signal in the low temperature regime and…
A derivation is given for the Vogel-Fulcher-Tammann thermal activation law for the glassy state of a bulk polymer. Our microscopic considerations involve the entropy of closed polymer molecular chains (i.e. polymer closed strings). For thin film polymer glasses, one obtains open polymer strings in that the boundary surfaces serve as possible string endpoint locations. The Vogel-Fulcher-Tammann thermal activation law thereby holds true for a bulk polymer glass but is modified in the neighborhood of the boundaries of thin film polymers.
We evaluate the mean escape time of overdamped particles over potential barriers in short-correlated quenched Gaussian disorder potentials in one dimension at low temperature. The thermally activated escape is very sensitive to the form of the \emph{tail} of the potential barrier probability distribution. We evaluate this tail by using the optimal fluctuation method. For monotone decreasing autocovariances we reproduce the tail obtained by Lopatin and Vinokur (2001). However, for nonmonotonic autocovariances of the disorder potential we show that the tail changes. It is much higher when the di…
Jumps between neighboring minima in the energy landscape of both homopolymeric and heteropolymeric chains are numerically investigated by determining the average escape time from different valleys. The numerical results are compared to the theoretical expression derived by Langer [J.S. Langer, Ann. Phys. 54 (1969) 258] with reference to a 2N-dimensional space. Our simulations indicate that the dynamics within the native valley is well described by a sequence of thermally activated process up to temperatures well above the folding temperature. At larger temperatures, systematic deviations from …
Cross slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross slip. However, due to its limited timescale, MD can only predict cross-slip rates in high-stress or high-temperature conditions. The transition state theory can predict the cross-slip rate over a broad range of stress and temperature conditions, …
We study relaxation dynamics of a three dimensional elastic manifold in random potential from a uniform initial condition by numerically solving the Langevin equation.We observe growth of roughness of the system up to larger wavelengths with time.We analyze structure factor in detail and find a compact scaling ansatz describing two distinct time regimes and crossover between them. We find short time regime corresponding to length scale smaller than the Larkin length $L_c$ is well described by the Larkin model which predicts a power law growth of domain size $L(t)$. Longer time behavior exhibit…
The period-average rate in the low frequency limit for thermally activated escape with periodic driving is derived in a closed analytical form. We define the low frequency limit as the one where there is no essential dependence on frequency so that the formal limit $Ω\to 0$ in the appropriate equations can be taken. We develop a perturbation theory of the action in the modulation amplitude and obtain a cumbersom but closed and tractable formula for arbitrary values of the modulation ampitude to noise intensity ratio $A/D$ except a narrow region near the bifurcation point and a simple analytica…
The effect of thermal fluctuations on spin-transfer switching has been studied for a broad range of time scales (sub-ns to seconds) in a model system, a uniaxial thin film nanomagnet. The nanomagnet is incorporated into a spin-valve nanopillar, which is subject to spin-polarized current pulses of variable amplitude and duration. Two physical regimes are clearly distinguished: a long pulse duration regime, in which reversal occurs by spin-transfer assisted thermal activation over an energy barrier, and a short time large pulse amplitude regime, in which the switching probability is determined b…
Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve magnetization patterns within nanomagnets and uses the Fast Multipole method to calculate dipole-dipole interactions efficiently. The thermal fluctuations play an essential part in the reversal process whenever the applied field is less than the zero-temperature coercive field. In this situation pillar-shaped nanomagnets are found to reverse through a local curling mo…
We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Kosmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)]. On the other hand, buckled shapes are energetically favorable already at pressures below the classic…
Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin term, and the Fast Multipole Method is used to calculate dipole-dipole interactions. It is feasible to simulate these dynamics on the nanosecond time scale for spatial discretizations that involve on the order of 10000 nodes using a desktop workstation. The nanoscale magnets considered here are single pillars with large aspect ratio. Hysteresis-loop simulat…
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an extern…
We review work by the authors on thermal activation in nanoscopic magnetic systems. These systems present unique difficulties in analyzing noise-induced escape over a barrier, including the presence of nonlocal interactions, nongradient terms in the energy functional, and dynamical textures as initial or saddle states. We begin with a discussion of magnetic reversal between single-domain configurations of the magnetization. Here the transition (saddle) state can be either a single-domain or a spatially varying (instanton-like) configuration, and depending on the system parameters can exhibit e…
We theoretically study thermally activated elementary dynamical processes that precede full structural relaxation in ultra-dense particle liquids interacting via strong short range attractive forces. Our approach is based on a microscopic theory formulated at the particle trajectory level built on the dynamic free energy concept and an explicit treatment of how attractions control physical bonding. Mean time scales for bond breaking, the early stage of cage escape, and a fixed non-Fickian displacement are analyzed in the repulsive glass, bonded repulsive (attractive) glass, fluid, and dense ge…
We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized ``phase'' one encounters two different scenarios: for moderate inelasticity, the jumps from one …
The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful interplay between elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling t…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyse it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regim…
