An alternative form of kinetic equations, involving the internal and free energies symmetrically, has been derived in the framework of the theory of vacancies. Dynamical nature of irreversible phenomena during formation and motion of defects (dislocations) has been analyzed by a computer experiment. Results of this simulation are then extended into a thermodynamic identity, involving the law of conservation of energy at interaction with an environment (the first law of thermodynamics) and the law of energy transformation in the internal degrees of freedom (relaxation). This identity is compared to the analogous Jarzynski identity. The approach is illustrated by simulation of processes during severe plastic deformation; the Rybin kinetic equation for this case has been derived.

Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in the presence of a confining magnetic field which varies with distance $\left|\vec{x}\right|$ to a “trap center,” proportionally to ${\left(\left|\vec{x}\right|/\ell \right)}^p$, where $p>0$. On a strip geometry, the competition between the “trap size” $\ell$ and the strip width $L$ is analyzed in the context of a generalized finite-size scaling ansatz. In the low-field regime $\ell ⪢L$, we use conformal-invariance concepts in conjunction with a linear-response approach to derive the appropriate ($p$-dependent) limit of the theory, which agrees very well with numerical results for magnetization profiles. For high fields $\ell \lesssim L$, correlation-length scaling data broadly confirm an existing picture of $p$-dependent characteristic exponents. Standard spin-1/2 and spin-1 Ising systems are considered, as well as the Blume-Capel model.

The response of a trapping overdamped monostable system to a harmonic perturbation is analyzed, in the context of stochastic resonance phenomenon. We consider the dynamics of a Brownian particle moving in a piecewise linear potential with a white Gaussian noise source. Based on linear-response theory and Laplace transform technique, analytical expressions of signal-to-noise ratio (SNR) and signal power amplification (SPA) are obtained. We find that the SNR is a nonmonotonic function of the noise intensity, while the SPA is monotonic. Theoretical results are compared with numerical simulations.

We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a potential well. The results apply for an arbitrary average rate of noise pulses, from slow pulse rates, where the noise acts on the system as strongly non-Gaussian, to high pulse rates, where the noise acts as effectively Gaussian.

Colloidal particles are trapped harmonically on the vertices of planar regular polygons, using optical tweezers. The particles interact with each other via hydrodynamic coupling, which can be described adequately by Oseen’s tensor. Because of the interaction, the dynamics of any individual sphere is complex. Thermal motion results in a spectrum of relaxation times. The configuration of a system of $N$ particles can be decomposed into $2N$ normal modes. In this work it is shown how to calculate these modes and their relaxation time scale analytically. The mathematical structure of the matrix of interaction leads to general properties for the symmetry of the normal modes and their dynamics, differing between the cases of even and odd $N$. The theory is compared to experiments performed on a range of rings with $3\le N\le 10$, varying also the trap stiffness and the distance between particles.

We analyze the evolution in thickness and radius of the film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit random fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configurational space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thicknesses and radi that can fluctuate. Our analysis is based on a Langevin-Brownian dynamics approach, which accounts for the thermodynamic and hydrodynamic interactions in the lubrication approximation. We examine the effect of parameters such as droplet size, interfacial mobility, and electrolyte concentration on the coalescence of small Brownian droplets. The results suggest that the coalescence times depend on a complex interplay between the thermodynamic and hydrodynamic interactions.

Oscillatory zoning (OZ) occurs in all major classes of minerals and also in a wide range of geological environments. It is caused by self-organization and describes fluctuations of the spatial chemical composition profile of the crystal. We present here a two-dimensional model of OZ based on our previous one-dimensional (1D) analysis and investigate whether the results of the 1D stability analysis remain valid. With the additional second dimension we were able to study the origin of the spatially homogeneous layer formation by linear stability analysis. Numerical solutions of the model are presented and the results of a Fourier analysis delivers a detailed understanding of the crystal growth behavior as well as the limits of the model. Effects beyond linear stability analysis are important to finally understand the final structure formation.

We analyze the coherence resonance phenomenon in an ensemble of noise-driven excitable neurons giving special attention to the role of the interaction topology. The neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale-free-like with dominating long-range connections and a network with mostly adjacent neurons connected. We found that besides an optimal noise intensity, also an optimal network configuration exists at which the largest average coherence of noise-induced spikes is achieved. Furthermore, we show that long- as well as short-range interactions between neurons should exist in order to achieve the optimal response of the neuronal network.

We analyze the dynamics toward cultural consensus in the Axelrod model on scale-free networks. By looking at the microscopic dynamics of the model, we are able to show how culture traits spread across different cultural features. We compare the diffusion at the level of cultural features to the growth of cultural consensus at the global level, finding important differences between these two processes. In particular, we show that even when most of the cultural features have reached macroscopic consensus, there are still no signals of globalization. Finally, we analyze the topology of consensus clusters both for global culture and at the feature level of representation.

We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability $p$ at every time instant. We observe that such a kind of coupling stabilizes the local fixed point of a circle map, with the resultant globally stable attractor providing a unique absorbing state. Interestingly, a continuous phase transition is observed from the absorbing state to spatiotemporal chaos via spatiotemporal intermittency for a range of values of $p$. It is interesting to note that the transition falls in class of directed percolation. Static and spreading exponents along with relevant scaling laws are found to be obeyed confirming the directed percolation universality class in spatiotemporal intermittency regime.

Whether statistics of intermittencies (between small and large eddies) in homogeneous and isotropic turbulence should be described by a logarithmic-Poisson, a logarithmic-stable probability density function, or other is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk, and random vortex stretching is established which may help to obtain new insights on this topic. A very simple relationship between the stability index of the Lévy stable law and Flory’s exponent stemming from statistics of linear polymer growth is established. Moreover, the scaling of turbulence intermittencies with Reynolds number is also explained and the overall picture is given of smallest vortex tubes of Kolmogorov length width (i.e., the smallest dissipative eddies) bent by bigger vortices of Taylor length scale (i.e., the mean dissipative eddies), themselves stretched by the bigger eddies in a continuous cascade. This results in both a simple and sound model with no fitting parameters required.

Dissipative particle dynamics with energy conservation (eDPD) was used to study natural convection via Rayleigh-Bénard (RB) problem and a differentially heated enclosure problem (DHE). The current eDPD model implemented the Boussinesq approximation to model the buoyancy forces. The eDPD results were compared to the finite volume solutions and it was found that the eDPD method predict the temperature and flow fields throughout the natural convection domains properly. The eDPD model recovered the basic features of natural convection, such as development of plumes, development of thermal boundary layers, and development of natural convection circulation cells (rolls). The eDPD results were presented via temperature isotherms, streamlines, velocity contours, velocity vector plots, and temperature and velocity profiles. Further useful quantities, such as Nusselt number was calculated from the eDPD results and found to be in good agreement with the finite volume calculations.

The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability $p$. In order to discriminate the better and worse opinions, we break the $Z_2$ symmetry $\left(\sigma =\pm 1\right)$ by giving a little more preference to the opinion $\sigma =1$. It is found that as $p$ becomes larger, introducing more complicated pattern of information flow channels, and as the network size $N$ becomes larger, the system eventually evolves to the state in which more voters agree on the better opinion, even though the voter at the top of the hierarchy keeps the worse opinion. We also find that the pure hierarchical tree makes opinion agreement very fast, while the final absorbing state can easily be influenced by voters at the higher ranks. On the other hand, although the ordering occurs much slower, the existence of complicated pattern of bidirectional information flow allows the system to agree on the better opinion.

The interaction of two counterpropagating solitons of equal amplitudes has been studied experimentally and numerically in a monolayer strongly coupled complex plasma. Complex plasmas are microparticle suspensions in ion-electron plasmas. It was found that the solitons are delayed after the collision. Solitons with higher amplitude experience longer delays. The amplitude of the overlapping solitons during the collision was less than the sum of the initial soliton amplitudes.

The statistics of self-avoiding random walks (SAWs), consisting of up to $N=1280$ steps, on deterministic fractal structures with infinite ramification, modeled by Sierpinski cubic lattices, in the presence of a finite temperature is investigated as a model for polymers absorbed on a disordered medium. Thereby, the three-dimensional Sierpinski sponge is defined by two types of sites with energy 0 and $ϵ>0$, respectively, yielding a deterministic fractal energy landscape. The probability distribution function of the end-to-end distance of SAWs is obtained and its scaling behavior studied. In the limiting case of temperature $T\to \infty$, the known behavior of SAWs on regular cubic lattices is recovered, while for $T\to 0$ the resulting scaling exponents are confronted with previous calculations for much shorter linear chains based on the exact enumeration technique. For finite temperatures, the structural behavior of SAWs in three dimensions is compared to its two-dimensional counterpart and found to be intermediate between the two limiting cases ($T\to 0$ and $T\to \infty$, respectively), where the characteristic exponents, however, display a nontrivial dependence on temperature.

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size $N$. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the zero-range process by including a pair exclusion. Each particle is associated with its own partner and particles of a pair are forbidden to stay at the same site. The pair exclusion is weak in that a particle interacts with only a single one among all others. It turns out that such a weak interaction changes the nature of condensation drastically. There appear a number of mesoscopic condensates: the mass of a condensate scales as $m_{\text{con}}\sim N^{1/2}$ and the number of condensates scales as $N_{\text{con}}\sim N^{1/2}$ with a logarithmic correction. These results are derived analytically through a mapping to a solvable model under a certain assumption and confirmed numerically.

We have studied the evolution of cellular structures in ${\text{Ge}}_{1-x}{\text{Si}}_x$ single-crystal growth as a function of process parameters. Because these structures are much larger than those occurring during the solidification of metals, we developed a modified phase-field method, which is able to handle these structure within reasonable computer times using the real material parameters. The model has been tested for computing equilibrium shapes of crystals, dendritic growth, and cellular growth of ${\text{Ni}}_x{\text{Cu}}_{1-x}$. We also performed classical molecular dynamics calculations in order to compute the diffusion coefficients of Si and Ge in melts of various compositions.

We consider many-site mutation-recombination models of molecular evolution, where fitness is a function of a Hamming distance from one (one-dimensional case) or two (two-dimensional case) sequences. For the one-dimensional case, we calculate the population distribution dynamics for a model with zero fitness and an arbitrary symmetric initial distribution and find an error threshold transition point in the single-peak fitness model for a given initial symmetric distribution. We calculate the recombination period in the case of a single-peak fitness function, when the original population is located at one sequence, at some Hamming distance from the peak configuration. Steady-state fitness is calculated with finite genome length corrections. We derive analytical equations for the two-dimensional mutation-recombination model.

We analyze the effects of noise correlations in the input to, or among, Bienenstock-Cooper-Munro neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.

The noninvasiveness of nonlinear optical imaging techniques is quantified in terms of the number of free electron generated in the laser-tissue interaction region per photon emitted into the nonlinear optical signal. For a broad variety of biomarker dyes and bioactivity reporter proteins, this ratio is shown to approach a critical value of unity for field intensities above $1\text{TW}/{\text{cm}}^2$. Closed-form analytical expressions for the ionization penalty function and the critical pulse repetition rate are derived for few-cycle laser pulses.