We investigate by Monte Carlo simulations density, diffusion, and structural anomalies of the simple two-dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also a variance of silica-like models. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy, and diffusivity anomalies for MB model. The orientational order parameters with three and six-fold symmetry were determined and maximum for each one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.

We propose a standing-wave-decomposition (SWD) approximation to Gaussian process (GP) regression. GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short ranged, the kernel matrix inversion can be replaced by analytic diagonalization using the SWD. We show that this approach applies to uni- and multidimensional input data, extends to include longer-range correlations, and the grid can be in a latent space and used as inducing points. Through simulations, we show that our approximate method applied to the squared exponential kernel outperforms existing methods in predictive accuracy per unit time in the regime where data are plentiful. Our SWD-GP is recommended for regression analyses where there is a relatively large amount of data and/or there are constraints on computation time.

Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The corresponding inference problems are challenging since the normalization constant (partition function) of the Ising or Potts distribution cannot be computed efficiently on large instances. Different ways to address this issue have resulted in a substantial amount of methodological literature. In this paper we investigate how these methods could be used on much larger data sets than studied previously. We focus on a central aspect, that in practice these inference problems are almost always severely undersampled, and the operational result is almost always a small set of leading predictions. We therefore explore an approach where the data are prefiltered based on empirical correlations, which can be computed directly even for very large problems. Inference is only used on the much smaller instance in a subsequent step of the analysis. We show that in several relevant model classes such a combined approach gives results of almost the same quality as inference on the whole data set. It can therefore provide a potentially very large computational speedup at the price of only marginal decrease in prediction quality. We also show that the results on whole-genome epistatic couplings that were obtained in a recent computation-intensive study can be retrieved by our approach. The method of this paper hence opens up the possibility to learn parameters describing pairwise dependences among whole genomes in a computationally feasible and expedient manner.

We studied glass transition in a nonvibrating granular system composed of magnetic steel beads under an unsteady magnetic field. In this model system, particle concentration and effective temperature can be changed independently. We analyzed several particle concentration cases. As concentration increases, the system goes from a fragile to a strong glass-forming liquid behavior and the regularity factor increases showing that the system becomes more regular. As the effective potential shows deeper wells, the fragility index decreases, and the regularity factor increases.

We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we consider a variety of different theoretical scenarios. These include multidefect chains and their ability to transmit, reflect, and especially trap energy. Moreover, they involve defects which are spatially separated and either statically or, more effectively, dynamically enable the confinement of energy between the separated defects. Wherever possible, comparisons of the experiments with numerical simulations as well as with theoretical intuition are also offered, to provide a justification for the observed findings.

This paper introduces improvements to an amplitude expansion of the phase-field-crystal model. An auxiliary field describing local grain rotation is introduced and used to enable the adaptive mesh to be coarsened in all grains, regardless of their orientation. Only a Cartesian representation of the amplitude equations is used.

We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse grain a detailed microscopic description into a previously developed internal state diffusive framework. The observables in the mesoscopic model correspond to solutions of macroscopic partial differential equations driven by stochastically varying diffusion fields in space and time. Analytical solutions and numerical experiments illustrate the framework.

By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor $\simeq 0.9$. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.

We show that the Ulam method applied to dynamical symplectic maps generates Ulam networks which belong to the class of small-world networks appearing for social networks of people, actors, power grids, biological networks, and Facebook. We analyze the small-world properties of Ulam networks on examples of the Chirikov standard map and the Arnold cat map showing that the number of degrees of separation, or the Erdös number, grows logarithmically with the network size for the regime of strong chaos. This growth is related to the Lyapunov instability of chaotic dynamics. The presence of stability islands leads to an algebraic growth of the Erdös number with the network size. We also compare the time scales related with the Erdös number and the relaxation times of the Perron-Frobenius operator showing that they have a different behavior.

We confront a network model of human aging and mortality in which nodes represent health attributes that interact within a scale-free network topology, with observational data that use both clinical and laboratory (preclinical) health deficits as network nodes. We find that individual health attributes exhibit a wide range of mutual information with mortality and that, with a reconstruction of their relative connectivity, higher-ranked nodes are more informative. Surprisingly, we find a broad and overlapping range of mutual information of laboratory measures as compared with clinical measures. We confirm similar behavior between most-connected and least-connected model nodes, controlled by the nearest-neighbor connectivity. Furthermore, in both model and observational data, we find that the least-connected (laboratory) nodes are damaged earlier than the most-connected (clinical) deficits. A mean-field theory of our network model captures and explains this phenomenon, which results from the connectivity of nodes and of their connected neighbors. We find that other network topologies, including random, small-world, and assortative scale-free networks, exhibit qualitatively different behavior. Our disassortative scale-free network model behaves consistently with our expanded phenomenology observed in human aging and so is a useful tool to explore mechanisms of and to develop predictive measures for human aging and mortality.

Receptor-mediated endocytosis is an ubiquitous process through which cells internalize biological or synthetic nanoscale objects, including viruses, unicellular parasites, and nanomedical vectors for drug or gene delivery. In passive endocytosis the cell plasma membrane wraps around the “invader” particle driven by ligand-receptor complexation. By means of theory and numerical simulations, here we demonstrate how particles decorated by freely diffusing and nonmutually interacting (ideal) ligands are significantly more difficult to wrap than those where ligands are either immobile or interact sterically with each other. Our model rationalizes the relationship between uptake mechanism and structural details of the invader, such as ligand size, mobility, and ligand-receptor affinity, providing a comprehensive picture of pathogen endocytosis and helping the rational design of efficient drug delivery vectors.

Elastic membranes composed of paramagnetic beads offer the possibility of assembling versatile actuators operated autonomously by external magnetic fields. Here we develop a theoretical framework to study shapes of such paramagnetic membranes under the influence of a fast precessing magnetic field. Their conformations are determined by the competition of the elastic and magnetic energies, arising as a result of their bending and the induced dipolar interactions between nearest-neighbors beads. In the harmonic approximation, the elastic energy is quadratic in the surface curvatures. To account for the magnetic energy we introduce a continuum limit energy, quadratic in the projections of the surface tangents onto the precession axis. We derive the Euler-Lagrange equation governing the equilibria of these membranes, as well as the corresponding stresses. We apply this framework to examine paramagnetic membranes with quasiplanar, cylindrical, and helicoidal geometries. In all cases we found that their shape, energy, and stresses can be modified by means of the parameters of the magnetic field, mainly by the angle of precession.

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with the external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.

We present a comprehensive Monte Carlo study of the ordering kinetics in the $d=2$ ferromagnetic $q$-state clock model with nonconserved Glauber dynamics. In agreement with previous studies we find that $q\ge 5$ is characterized by two phase transitions occurring at temperatures $T_c^1$ and $T_c^2$ ($T_c^2<T_c^1$). Phase-ordering kinetics is then investigated by rapidly quenching the system in two phases, in the quasi-long-range ordered phase (QLRO), where $T_c^2<T<T_c^1$, and in the long-range ordered phase (LRO), where $T<T_c^2$, $T$ being the quench temperature. Our numerical data for equal time spatial correlation function $C(\mathbf{r},t)$ and structure factor $S(k,t)$ support dynamical scaling. Quench in the LRO regime is characterized by a crossover from a preasymptotic growth driven by the annealing of both vortices and interfaces to an interface driven growth at the asymptotic regime with growth exponent $n\simeq 0.5$. In the QLRO quench regime, domains coarsen mainly via annihilation of point defects and our length-scale data for $q=9$, 12, and 20 suggests a $R\left(t\right)\sim {(t/lnt)}^{1/2}$ growth law for the $q$-state clock model in the QLRO phase.

We present here the nonequilibrium dynamics of the recently studied quasiperiodic Ising model. The zero temperature phase diagram of this model mainly consists of three phases, where each of these three phases can have extended, localized, or critically delocalized low-energy excited states. We explore the nature of excitations in these different phases by studying the evolution of entanglement entropy after performing sudden quenches of different strengths to different phases. Our results on nonequilibrium dynamics of entanglement entropy are concurrent with the nature of excitations predicted in Chandran and Laumann [Phys. Rev. X 7, 031061 (2017)].

Time-averaged spatially resolved measurements are used in many fields of physics to determine spatial distributions of a physical quantity. Although one could think that time averaging suppresses all information on time variation, there are some situations in which a link can be established between time averaging and time variability. In this paper, we consider a simple system composed of a particle bunch that moves in space without deforming, and a detector placed at a point in space. The detector continuously counts the number of particles in its neighborhood. Upon sampling, the detector signal gives rise to a time series with, in general, nonvanishing variance. Time series obtained by placing the detector at different locations can then be used to obtain a time-average distribution of the number of particles by computing the time average of all the time series. We show that there is a close relationship between this average profile and higher-order statistics of the time series, including the variance and skewness. We also show a simple procedure by which individual time series can be used to determine features of the shape of the particle bunch.

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modeling and computational challenges. In a previous paper, we derived simplified electro-neutral (EN) models in one-dimensional space where the thin boundary layers are replaced by effective boundary conditions. In this paper, we extend our analysis to the multidimensional case where the EN model enjoys even greater advantages. First, it is much cheaper to solve the EN models numerically. Second, EN models are easier to deal with compared with the original PNP system, therefore it is also easier to derive macroscopic models for cellular structures using EN models. The multi-ion case with a general boundary is considered for a variety of boundary conditions including either Dirichlet or flux boundary conditions. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to the EN system for the bulk region. To validate the EN models, numerical computations are carried out for both the EN and original PNP system, including the propagation of action potential for both myelinated and unmyelinated axons. Our results show that solving the EN models is much more efficient than the original PNP system.

The circadian oscillator exhibits remarkably high temporal precision, despite its exposure to several fluctuations. The central mechanism that protects the oscillator from fluctuations is a collective enhancement of precision where a population of coupled oscillators displays higher temporal precision than that achieved without coupling. Since coupling is essentially information exchange between oscillators, we herein investigate the relation between the temporal precision and the information flow between oscillators in the linearized Kuramoto model by using stochastic thermodynamics. For general coupling, we find that the temporal precision is bounded from below by the information flow. We generalize the model to incorporate a time-delayed coupling and demonstrate that the same relation also holds for the time-delayed case. Furthermore, the temporal precision is demonstrated to be improved in the presence of the time delay, and we show that the increased information flow is responsible for the time-delay-induced precision improvement.