The vortex-excitation energy on a sphere can be obtained by using the stereographic projection. By applying this method, we calculate the energy needed to create a vortex on a surface with a constant negative curvature. It is found that the energy is a linear function of the radius of the vortex. In accordance with this result, the interaction energy between a pair of vortices is also found to change linearly with the vortex separation distance. Explicit vortex configurations are obtained numerically with this interaction.

We have performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional ST's applicability to dealing with phase transitions and study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus this simulation can be referred to as simulated tempering and magnetizing (STM). We also performed simulated magnetizing (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. As discussed in previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Flipping of the entire magnetization did not occur in the SM simulations under the critical temperature $T_c$ in large-lattice-size simulations; however, the phase changed through the high-temperature region in the STM simulations. Thus the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study a wide area of the phase space. We discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior is clearly observed in the simulations, in agreement with the theoretical implications.

In dense colloids it is commonly assumed that hydrodynamic interactions do not play a role. However, a found theoretical quantification is often missing. We present computer simulations that are motivated by experiments where a large colloidal particle is dragged through a colloidal crystal. To qualify the influence of long-ranged hydrodynamics, we model the setup by conventional Langevin dynamics simulations and by an improved scheme with limited hydrodynamic interactions. This scheme significantly improves our results and allows to show that hydrodynamics strongly impacts the development of defects, the crystal regeneration, as well as the jamming behavior.

Repeats are frequently found in known protein sequences. The level of sequence conservation in tandem repeats correlates with their propensities to be intrinsically disordered. We employ a coarse-grained model of a protein with a two-letter amino acid alphabet, hydrophobic (H) and polar (P), to examine the sequence-structure relationship in the realm of repeated sequences. A fraction of repeated sequences comprises a distinct class of bad folders, whose folding temperatures are much lower than those of random sequences. Imperfection in sequence repetition improves the folding properties of the bad folders while deteriorating those of the good folders. Our results may explain why nature has utilized repeated sequences for their versatility and especially to design functional proteins that are intrinsically unstructured at physiological temperatures.

A quantitative phase-field model is developed for simulating microstructural pattern formation in nonisothermal solidification in dilute multicomponent alloys with arbitrary thermal and solutal diffusivities. By performing the matched asymptotic analysis, it is shown that the present model with antitrapping current terms reproduces the free-boundary problem of interest in the thin-interface limit. Convergence of the simulation outcome with decreasing the interface thickness is demonstrated for nonisothermal free dendritic growth in binary alloys and isothermal and nonisothermal free dendritic growth in a ternary alloy.

By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for their existence and investigate the interplay between cascade and cluster forms. As a result, we demonstrate how to generate many more hybrid rogue wave solutions, including semicircular clusters that resemble claws.

Estimation of model parameters is as important as model building, but is often neglected in model studies. Here we show that despite the existence of well known results on parameter estimation in a simple homogenous Ornstein-Uhlenbeck process, in most practical situations the methods suffer greatly from finite sample sizes and especially the estimator of the time constant of the system is degraded. Therefore an alternative solution is of paramount importance. We present such a solution based on perturbation of the system, observing trajectories far from equilibrium. The results are illustrated on computer experiments based on applications in neuroscience and pharmacokinetics, which show a striking improvement of the quality of estimation. The results are important for judicious designs of experiments to obtain maximal information from each data point, especially when samples are expensive or difficult to obtain.

For work-producing heat engines, or work-consuming refrigerators and heat pumps, the percentage decrease caused by friction in their efficiencies, or coefficients of performance (COP's), is approximately given by the ratio $W_{\mathrm{fric}}/W$ between the work spent against friction forces and the work performed by, or delivered to, the working fluid. This universal scaling, which applies in the limit of small friction ($W_{\mathrm{fric}}/W\lesssim 20\%$) and when the engine's figures of merit (FOM's, either efficiencies or COP's) do not come too close to unity (no higher than, say, $0.5$ in the case of heat-engine efficiencies), allows a simple and quick estimate of the impact that friction losses can have on the FOM's of thermal engines and plants, or of the level of those losses from the observed and predicted FOM's. In the case of refrigerators and heat pumps, if $W_{\mathrm{fric}}/W\lesssim 20\%$ is not ensured (actually a condition that can be largely relaxed for heat engines), the COP percentage decrease due to friction approaches asymptotically $(W_{\mathrm{fric}}/W)/(1+W_{\mathrm{fric}}/W)$ instead of $W_{\mathrm{fric}}/W$. Estimates for the level of frictional losses using the Carnot (or, for heat engines and power plants only, the Curzon-Ahlborn) predictions and observed FOM's of real power plants, heat engines, refrigerators, and heat pumps show that they usually operate in domains where these behaviors are valid.

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point ($B$), a zero-temperature critical point ($Z$), a critical end point ($E$), and a triple point ($TP$). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.

Zhu et al. [L. Zhu, C. W. Brian, S. F. Swallen, P. T. Straus, M. D. Ediger, and L. Yu, Phys. Rev. Lett. 106, 256103 (2011)] measured the surface self-diffusion for an organic glass former, indomethacin, and found surface diffusion is more than 10${}^6$ times faster than bulk diffusion at temperatures around $T_g$. With the help of dielectric relaxation and differential scanning calorimetry measurements on bulk indomethacin, and analysis of the data using the coupling model, we provide a quantitative explanation. We find the bulk α-relaxation time is longer than the primitive relaxation time also by about six orders of magnitude in a range of temperature above and below the bulk $T_g$. Thus, the cause of the fast surface diffusion is the nearly vanishing of intermolecular coupling of relaxation and diffusion at the surface. The results of related experimental studies of enhanced relaxation and diffusion at the surface of other glass formers also have been analyzed and quantitatively explained. Our predictions on surface diffusion from the coupling model are compared with that given by the random first order transition theory.

Various experimental studies in zero gravity have been reported in the literature for generation of superior quality crystals due to the importance of convective transport on protein crystal quality. However, limited experimental and numerical studies are available in the literature for a complete characterization of transport phenomena during the protein crystal growth process. The present investigation reports experimental results on convective motion inside the droplet during protein crystallization by the vapor diffusion method. Lysozyme crystals are grown using a sitting drop method and micro-particle image velocimetry is used for investigating the detailed hydrodynamics inside the droplet. Dynamic evolution of the flow field for the complete crystal growth process, i.e., during the prenucleation, nucleation, and postnucleation stage, is reported. Various flow transitions are observed during the complete cycle of the protein crystal growth process. Significant Marangoni convection is observed during the prenucleation period followed by buoyancy-driven convection during the postnucleation period. The Marangoni convection flow patterns observed during the prenucleation stage match those of evaporating droplets. The postnucleation convection patterns are similar to those of ethanol-water mixture evaporation with high ethanol concentration.

We consider the competitive population dynamics of two species described by the Lotka-Volterra model in the presence of spatial diffusion. The model is described by the diffusion coefficient ($d_{\alpha }$) and proliferation rate ($r_{\alpha }$) of the species $\alpha$ ($\alpha =1,2$ is the species label). Propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. It is found that the wave profiles and wave speeds are determined by the speed parameters, $v_{\alpha }\equiv 2\sqrt{d_{\alpha }{r}_{\alpha }}$, of the two species, and the phase diagrams for various inter- and intracompetitive scenarios are determined. The steady wave front speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. The effect of the intermediate stationary state is investigated and propagating wave profiles beyond the simple Fisher wave fronts are revealed. The wave front speed of a species can display abrupt increase as its speed parameter is increased. In particular for the case in which both species are aggressive, our results show that the speed parameter is the deciding factor that determines the ultimate surviving species, in contrast to the case without diffusion in which the final surviving species is decided by its initial population advantage. Possible relations to the biological relevance of modeling cancer development and wound healing are also discussed.

We define a cellular automaton where a resting cell excites if number of its excited neighbors belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbors in the cell's neighborhood. We calculate excitability of a cell as a number of possible neighborhood configurations that excite the resting cell. We call cells with maximal values of excitability conductive. In exhaustive search of functions of excitation interval updates we select functions which lead to formation of connected configurations of conductive cells. The functions discovered are used to design conductive, wirelike, pathways in initially nonconductive arrays of cells. We demonstrate that by positioning seeds of growing conductive pathways it is possible to implement a wide range of routing operations, including reflection of wires, stopping wires, formation of conductive bridges, and generation of new wires in the result of collision. The findings presented may be applied in designing conductive circuits in excitable nonlinear media, reaction-diffusion chemical systems, neural tissue, and assemblies of conductive polymers.

Nonequilibrium processes require that the density operator of an interacting system with Hamiltonian $\mathcal{H}\left(t\right)={\mathcal{H}}^0\left(t\right)+\lambda \mathcal{V}$ converges and produces entropy. Employing projection operators in the state space, the density operator is developed to all orders of perturbation and then resummed. In contrast to earlier treatments by Van Hove [Physica 21, 517 (1955)] and others [U. Fano, Rev. Mod. Phys. 29, 74 (1959); U. Fano, in Lectures on the Many-Body Problem, Vol 2, edited by E. R. Caniello (Academic Press, New York, 1964); R. Zwanzig, in Lectures in Theoretical Physics, Vol. III, edited by W. E. Britten, B. W. Downs, and J. Downs (Wiley Interscience, New York, 1961), pp. 116–141; K. M. Van Vliet, J. Math. Phys. 19, 1345 (1978); K. M. Van Vliet, Can. J. Phys. 56, 1206 (1978)], closed expressions are obtained. From these we establish the time-reversal symmetry property $P(\gamma ,t|{\gamma }^{\prime },t^{\prime })=\tilde{P}({\gamma }^{\prime },t^{\prime }|\gamma ,t)$, where the tilde refers to the time-reversed protocol; also a nonstationary Markovian master equation is derived. Time-reversal symmetry is then applied to thermostatted systems yielding the Crooks-Tasaki fluctuation theorem (FT) and the quantum Jarzynski work-energy theorem, as well as the general entropy FT. The quantum mechanical concepts of work and entropy are discussed in detail. Finally, we present a nonequilibrium extension of Mazo's lemma of linear response theory, obtaining some applications via this alternate route.

In this paper we report a theoretical model based on Green's functions, Floquet theory, and averaging techniques up to second order that describes the dynamics of parametrically driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincaré map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects causes most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.

We study the cooperation problem in the framework of evolutionary game theory by using the prisoner's dilemma as a metaphor of the problem. By considering the growing process of the system and individuals with imitation capacity, we show conditions that allow the formation of highly cooperative networks of any size and topology. By introducing general considerations of real systems, we reduce the required conditions for cooperation to evolve, which approaches the benefit-cost ratio $r$ for the theoretical minimum $r=1$ when the mean connectivity of the individuals is increased. Throughout the paper, we distinguish different mechanisms that allow the system to maintain high levels of cooperation when the system grows by incorporation of defectors. These mechanisms require heterogeneity among individuals for cooperation to evolve. However, the required benefit-cost ratio and heterogeneities are drastically reduced as compared to those required for static networks.

We numerically investigate the mechanism of super rebounds (rebounds in which the restitution coefficient is larger than unity) for head-on collisions between nanoclusters. It is confirmed that the temperature and the entropy of the nanocluters decrease after the super rebounds by our molecular dynamics simulations. It is also found that the initial metastable structure plays a key role for the emergence of the super rebounds.

By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.

We study the interplay of topology and dynamics in a neural network connected with spike-timing-dependent plasticity (STDP) synapses. Stimulated with periodic spike trains, the STDP-driven network undergoes a synaptic pruning process and evolves to a residual network. We examine the variation of topological and dynamical properties of the residual network by varying two key parameters of STDP: synaptic delay and the ratio between potentiation and depression. Our extensive numerical simulations of the leaky integrate-and-fire model show that there exists two regions in the parameter space. The first corresponds to fixed-point configurations, where the distribution of peak synaptic conductances and the firing rate of neurons remain constant over time. The second corresponds to oscillating configurations, where both topological and dynamical properties vary periodically, which is a result of a fixed point becoming a limit cycle via a Hopf bifurcation. This leads to interesting questions regarding the implications of these rhythms in the topology and dynamics of the network for learning and cognitive processing.