We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model, which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a $q$-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration $c$ defined as the ratio of the number of Potts spins $N_s$ to the total number of lattice sites $N_L=N_x\times N_y\times N_z$. Taking into account the attractive interaction between the nearest-neighboring Potts spins, we study the phase transitions as functions of various physical parameters such as the temperature, the shape of the recipient, and the spin concentration. We show that as the temperature increases, surface spins are detached from the solid phase to form a gas in the empty space. Surface order parameters indicate different behaviors depending on the distance to the surface. At high temperatures, if the concentration is high enough, the interior spins undergo a first-order phase transition to an orientationally disordered phase. The mean-field results are shown as functions of temperature, pressure, and chemical potential, which confirm in particular the first-order character of the transition.

We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this “form invariance” holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter $\alpha$ approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time-integrated) difference between entrance rate and escape rate in mesoscopic jump systems. Such inflow rate, which is even under time reversal, represents the discrete-state equivalent of the phase-space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.

We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model in which the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization-group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.

We investigate the phenomenon of protein-induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane-bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free-energy barrier increases with an increase in the curvature-field strength (i.e., of protein-membrane interactions) and also with an increase in membrane tension.

We present an analytically solvable model for self-assembly of a molecular complex on a filament. The process is driven by a seed molecule that undergoes facilitated diffusion, which is a search strategy that combines diffusion in three dimensions and one dimension. Our study is motivated by single-molecule-level observations revealing the dynamics of transcription factors that bind to the deoxyribonucleic acid at early stages of transcription. We calculate the probability that a complex made up of a given number of molecules is completely formed, as well as the distribution of completion times, upon the binding of a seed molecule at a target site on the filament (without explicitly modeling the three-dimensional diffusion that precedes binding). We compare two different mechanisms of assembly where molecules bind in sequential and random order. Our results indicate that while the probability of completion is greater for random binding, the completion time scales exponentially with the size of the complex; in contrast, it scales as a power law or slower for sequential binding, asymptotically. Furthermore, we provide model predictions for the dissociation and residence times of the seed molecule, which are observables accessible in single-molecule tracking experiments.

We present a financial market model, characterized by self-organized criticality, that is able to generate endogenously a realistic price dynamics and to reproduce well-known stylized facts. We consider a community of heterogeneous traders, composed by chartists and fundamentalists, and focus on the role of informative pressure on market participants, showing how the spreading of information, based on a realistic imitative behavior, drives contagion and causes market fragility. In this model imitation is not intended as a change in the agent's group of origin, but is referred only to the price formation process. We introduce in the community also a variable number of random traders in order to study their possible beneficial role in stabilizing the market, as found in other studies. Finally, we also suggest some counterintuitive policy strategies able to dampen fluctuations by means of a partial reduction of information.

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), $S\left(f\right)\sim f^{-\beta }$, a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent $\alpha$, which satisfies the scaling relation $\alpha =(\beta +1)/2$; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by $m+1$, where $m$ is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve the scale distortion by introducing the corrected time scale in the DFA corresponding to the inverse of the frequency scale in the PSD. In addition, our analytical approach makes it possible to characterize variants of the DFA using different types of detrending. As an application, properties of the detrending moving average algorithm are discussed.

We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can propagate with a constant velocity along the vortex core without any deformation. Stability of the soliton under a small perturbation is established numerically. Two such solitons moving along the vortex core can undergo a quasielastic collision at medium velocities. Possibilities of forming such a 2D spatial soliton in the core of a vortical beam are discussed.

We suggest an analytical approach to the adaptive thresholding in a shape anomaly detection problem. We find an analytical expression for the distribution of the cosine similarity score between a reference shape and an observational shape hindered by strong measurement noise that depends solely on the noise level and is independent of the particular shape analyzed. The analytical treatment is also confirmed by computer simulations and shows nearly perfect agreement. Using this analytical solution, we suggest an improved shape anomaly detection approach based on adaptive thresholding. We validate the noise robustness of our approach using typical shapes of normal and pathological electrocardiogram cycles hindered by additive white noise. We show explicitly that under high noise levels our approach considerably outperforms the conventional tactic that does not take into account variations in the noise level.

We experimentally probe the anisotropy of weakly vibrated flowing granular media. Depending on the driving parameters—flow rate and vibration strength—this anisotropy varies significantly. We show how the anisotropy collapses when plotted as a function of the driving stresses, uncovering a direct link between stresses and anisotropy. Moreover, our data suggest that for small anisotropies, the shear stresses vanish. Anisotropy of the fabric of granular media thus plays a crucial role in determining the rheology of granular flows.

We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as $\sim t^{\frac{1}{2}}$, as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability.

Using the replica method, we develop an analytical approach to compute the characteristic function for the probability ${\mathcal{P}}_N(K,\lambda )$ that a large $N\times N$ adjacency matrix of sparse random graphs has $K$ eigenvalues below a threshold $\lambda$. The method allows to determine, in principle, all moments of ${\mathcal{P}}_N(K,\lambda )$, from which the typical sample-to-sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with $N\gg 1$ for $\left|\lambda \right|>0$, with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a nonmonotonic behavior as a function of $\lambda$. These results contrast with rotationally invariant random matrices, where the index variance scales only as $lnN$, with an universal prefactor that is independent of $\lambda$. Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.

Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.

Solid-liquid phase transitions in three-dimensional (3D) and two-dimensional (2D) Yukawa systems were studied numerically and analytically, including the melting of the fcc and bcc 3D lattices, and of a hexagonal primitive (hp) 2D lattice. An approach is proposed for the determination of the melting lines in these systems. The suggested approach takes into account the nonlinearity (anharmonicity) of pair interaction forces and allows one to correctly predict the conditions of melting for 3D and 2D crystal systems. The obtained results are compared with the existing theoretical and numerical data.

We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent $\mu +1$. Assuming that the walker moves in the presence of a distribution $a\left(x\right)$ of targets (traps) depending on the spatial coordinate $x$, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions $a\left(x\right)\sim x^{-\alpha }$ and we find that, as long as $\mu <\alpha$, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.

Based on an analysis of Feynman's path integral formulation of the propagator, a relative criterion is proposed for validity of a semiclassical approach to the dynamics near critical points in a class of systems undergoing quantum phase transitions. It is given by an effective Planck constant, in the relative sense that a smaller effective Planck constant implies better performance of the semiclassical approach. Numerical tests of this relative criterion are given in the $XY$ model and in the Dicke model.

Numerical simulations of time-dependent stochastic failure of fiber network have been performed by using a central-force, triangular lattice model. This two-dimensional (2D) network can be seen as the next level of structural hierarchy to fiber bundles, which have been investigated for many years both theoretically and numerically. Unlike fiber bundle models, the load sharing of the fiber network is determined by the network mechanics rather than a preassigned rule, and its failure is defined as the point of avalanche rather than the total fiber failure. We have assumed that the fiber in the network follows Coleman's probabilistic failure law [B. D. Coleman, J. Appl. Phys. 29, 968 (1958)] with the Weibull shape parameter $\beta =1$ (memory less fiber). Our interests are how the fiber-level probabilistic failure law is transformed into the one for the network and how the failure characteristics and disorders on the fiber level influence the network failure response. The simulation results showed that, with increasing the size of the network $\left(N\right)$, weakest-link scaling (WLS) appeared and each lifetime distribution at a given size approximately followed Weibull distribution. However, the scaling behavior of the mean and the Weibull shape parameter clearly deviate from what we can predict from the WLS of Weibull distribution. We have found that a characteristic distribution function has, in fact, a double exponential form, not Weibull form. Accordingly, for the 2D network system, Coleman's probabilistic failure law holds but only approximately. Comparing the fiber and network failure properties, we found that the network structure induces an increase of the load sensitivity factor $\rho$ (more brittle than fiber) and Weibull shape parameter $\beta$ (less uncertainty of lifetime). Superimposed disorders on the fiber level reduce all these properties for the network.

The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature $T_{\mathrm{cr}}$ increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive $1/r^{18}$ potential.

Cell division through proper spindle formation is one of the key puzzles in cell biology. In most mammalian cells, chromosomes spontaneously arrange to achieve a stable bipolar spindle during metaphase which eventually ensures proper segregation of the DNA into the daughter cells. In this paper, we present a robust three-dimensional mechanistic model to investigate the formation and maintenance of a bipolar mitotic spindle in mammalian cells under different physiological constraints. Using realistic parameters, we test spindle viability by measuring the spindle length and studying the chromosomal configuration. The model strikingly predicts a feature of the spindle instability arising from the insufficient intercentrosomal angular separation and impaired sliding of the interpolar microtubules. In addition, our model successfully reproduces chromosomal patterns observed in mammalian cells, when activity of different motor proteins is perturbed.