Molecular dynamics is often considered as a numerical experiment. The error bars on the results are therefore mandatory, but sometimes difficult to determine and computationally demanding. As a low-cost approach, we describe the application of the bootstrap (BS) method to the quantification of uncertainties pertaining to the time correlation functions. We chose the autocorrelation functions of velocity and interdiffusion current for a binary ionic mixture as a test bed, and we assessed the merit of the Darken approximation relating both of them. The intrinsic errors related to phase space sampling is investigated comparing the BS method with the reference method of replica. We also study how the BS method can assist in addressing the finite-size effects.

The Gaussian orthogonal ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. In particular, it has often been invoked to explain the fluctuations in decay rates that follow the $\chi$-squared distribution for one degree of freedom, as originally proposed by Brink and by Porter and Thomas. However, we find that the coupling to the decay channels can change the effective number of degrees of freedom from one to two. Our conclusions are based on a configuration-interaction Hamiltonian originally constructed to test the validity of transition-state theory, also known as the Rice-Ramsperger-Kassel-Marcus theory in chemistry. The internal Hamiltonian consists of two sets of GOE reservoirs connected by an internal channel. We find that the effective number of degrees of freedom depends on the control parameter $\rho \mathrm{\Gamma }$, where $\rho$ is the level density in the first reservoir and $\mathrm{\Gamma }$ is the level decay width. The distribution for two degrees of freedom is a well-known property of the Gaussian unitary ensemble (GUE); our model demonstrates that the GUE fluctuations can be present under much milder conditions. Our treatment of the model permits an analytic derivation for $\rho \mathrm{\Gamma }\gtrsim 1$.

We consider a general model exhibiting type-I excitability mediated by a homoclinic and a saddle node on the invariant circle bifurcations. We show how the distinct properties of type-I with respect to type-II excitability confer unique features to traveling pulses in excitable media. They inherit the characteristic divergence of type-I excitable trajectories at threshold exhibiting analogous scalings in the spatial thickness of the pulses. Our results pave the way to identify basic underlying mechanisms behind type-I excitable pulses based solely on the characteristics of the pulse.

We explore Kapitza thermal resistance on the boundary between two homogeneous chain fragments with different characteristics. For a linear model, an exact expression for the resistance is derived. In the generic case of frequency mismatch between the domains, the Kapitza resistance is well defined in the thermodynamic limit. At the same time, in the linear chain, the resistance depends on the thermostat properties and therefore is not a local property of the considered domain boundary. Moreover, if the temperature difference at the ends of the chain is fixed, then neither the temperature drop at the domain boundary nor the heat flux depend on the system size; for the normal transport, one expects the scaling $N^{–1}$ for both. For specific assessment, we consider the case of an isotopic boundary—only the masses in different domains are different. If the domains are nonlinear, but integrable (Toda lattice, elastically colliding particles), the anomalies are similar to the case of linear chain, with the addition of well-articulated thermal dependence of the resistance. For the case of elastically colliding particles, this dependence follows a simple scaling law $R_k\sim T^{-1/2}$. For Fermi-Pasta-Ulam domains, both the temperature drop and the heat flux decrease with the chain length, but with different exponents, so the resistance vanishes in the thermodynamic limit. For the domains comprised of rotators, the thermal resistance exhibits the expected normal behavior.

The non-Markovian dynamics of a charged particle confined in the harmonic oscillator and linearly coupled to a neutral bosonic heat bath is investigated in the external uniform magnetic field. The analytical expressions are derived for the time-dependent and asymptotic orbital angular momenta. The transition from non-Markovian dynamics to Markovian dynamics and the transition from a confined charge particle to a free charge particle are considered. The orbital diamagnetism of graphene in a dissipative environment and an external uniform magnetic field is studied and compared with existing experimental data. The results are presented for the electric conductivity and resonance behavior of the mass magnetization in graphene.

The relationship between the eigenspectrum of Ising and $XY$ quantum chains is well known. Although the Ising model has a $Z\left(2\right)$ symmetry and the $XY$ model a $U\left(1\right)$ symmetry, both models are described in terms of free-fermionic quasiparticles. The fermionic quasienergies are obtained by means of a Jordan-Wigner transformation. On the other hand, there exists in the literature a huge family of $Z\left(N\right)$ quantum chains whose eigenspectra, for $N>2$, are given in terms of free parafermions, and they are not derived from the standard Jordan-Wigner transformation. The first members of this family are the $Z\left(N\right)$ free-parafermionic Baxter quantum chains. In this paper, we introduce a family of $XY$ models that, beyond two-body, also have $N$-multispin interactions. Similar to the standard $XY$ model, they have a $U\left(1\right)$ symmetry and are also solved by the Jordan-Wigner transformation. We show that with appropriate choices of the $N$-multispin couplings, the eigenspectra of these $XY$ models are given in terms of combinations of $Z\left(N\right)$ free-parafermionic quasienergies. In particular, all the eigenenergies of the $Z\left(N\right)$ free-parafermionic models are also present in the related free-fermionic $XY$ models. The correspondence is established via the identification of the characteristic polynomial, which fixes the eigenspectrum. In the $Z\left(N\right)$ free-parafermionic models, the quasienergies obey an exclusion circle principle that is not present in the related $N$-multispin $XY$ models.

We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase-separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens, which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that superuniversality does not hold in our system. The role of annealed disorder on the nonequilibrium aging dynamics is studied qualitatively by computing the two-time order-parameter autocorrelation function. The decay of the correlation function slows down significantly with the disorder. This quantity exhibits scaling laws with respect to the ratio of the domain length at the observation time and the age of the system. We find the scaling laws hold good for the disordered system and are therefore robust and generic to such segregating fluid mixtures.

Liquid crystal networks exploit the coupling between the responsivity of liquid crystalline mesogens, e.g., to electric fields, and the (visco)elastic properties of a polymer network. Because of this, these materials have been put forward for a wide array of applications, including responsive surfaces such as artificial skins and membranes. For such applications, the desired functional response must generally be realized under strict geometrical constraints, such as provided by supported thin films. To model such settings, we present a dynamical, spatially heterogeneous Landau-type theory for electrically actuated liquid crystal network films. We find that the response of the liquid crystal network permeates the film from top to bottom, and illustrate how this affects the timescale associated with macroscopic deformation. Finally, by linking our model parameters to experimental quantities, we suggest that the permeation rate can be controlled by varying the aspect ratio of the mesogens and their degree of orientational order when crosslinked into the polymer network, for which we predict a single optimum. Our results contribute specifically to the rational design of future applications involving transport or on-demand release of molecular cargo in liquid crystal network films.

The concept of kirigami has been extensively utilized to design deployable structures and reconfigurable metamaterials. Despite heuristic utilization of classical kirigami patterns, the gap between complex kirigami tessellations and systematic design principles still needs to be filled. In this paper, we develop a unified design method for deployable quadrilateral kirigami tessellations perforated on flat sheets with different topologies. This method is based on the parametrization of kirigami patterns formulated as the solution of a linear equation system. The geometric constraints for the deployability of parameterized cutting patterns are given by a unified theorem covering different topologies of the flat sheets. As an application, we employ the design method to achieve desired shapes along the deployment path of kirigami tessellations, while preserving the topological characteristics of the flat sheets. Our approach introduces interesting perspectives for the topological design of kirigami-inspired structures and metamaterials.

The mechanisms by which an organ regulates its growth are not yet fully understood, especially when the cells are closely packed as in epithelial tissues. We explain growth arrest as a collective dynamical transition in coupled oscillators on disordered lattices. As the cellular morphologies become homogeneous over the course of development, the signals induced by cell-cell contact increase beyond a critical value that triggers coordinated cessation of the cell-cycle oscillators driving cell division. Thus, control of cell proliferation is causally related to the geometry of cellular packing.

We consider a harmonic oscillator under periodic driving and coupled to two harmonic-oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup, which allows us to study the unitary evolution of the system and the baths up to a time when the periodic steady state emerges in the system. We characterize this periodic steady state, and we show that, by tuning the system and the bath parameters, one can turn this system from an engine to an accelerator or even to a heater. The possibility to study the unitary evolution of the system and baths also allows us to evaluate the steady correlations that build between the system and the baths, and correlations that grow between the baths.

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal test beds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wave packets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend effect. Furthermore, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective “impurities.” This behavior serves as a new mechanism for reversibly programming the dynamic response of bistable chains.

Message-passing theories have proved to be invaluable tools in studying percolation, nonrecurrent epidemics, and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix, whose largest eigenvalue, the corresponding eigenvector, and the closely related nonbacktracking centrality play a central role in determining how the given dynamical model behaves. Here we propose a degree-class-based method to approximate these quantities using a smaller matrix related to the joint degree-degree distribution of neighboring nodes. Our findings suggest that in most networks, degree-degree correlations beyond nearest neighbor are actually not strong, and our first-order description already results in accurate estimates, particularly when message-passing itself is a good approximation to the original model in question, that is, when the number of short cycles in the network is sufficiently low. We show that localization of the nonbacktracking centrality is also captured well by our scheme, particularly in large networks. Our method provides an alternative to working with the full nonbacktracking matrix in very large networks where this may not be possible due to memory limitations.

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on a fcc lattice which explicitly takes into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison with standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing makes polymer dynamics faster provided the characteristic timescale of the process is smaller than the typical timescale for chain relaxation in the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

Elastohydrodynamic models, that describe the interaction between a thin sheet and a fluid medium, have been proven successful in explaining the complex behavior of biological systems and artificial materials. Motivated by these applications we study the quasistatic deformation of a thin sheet that is confined between the two sides of a closed chamber. The two parts of the chamber, above and below the sheet, are filled with an ideal gas. We show that the system is governed by two dimensionless parameters, $\mathrm{\Delta }$ and $\eta$, that account respectively for the lateral compression of the sheet and the ratio between the amount of fluid filling each part of the chamber and the bending stiffness of the sheet. When $\eta \ll 1$ the bending energy of the sheet dominates the system, the pressure drop between the two sides of the chamber increases, and the sheet exhibits a symmetric configuration. When $\eta \gg 1$ the energy of the fluid dominates the system, the pressure drop vanishes, and the sheet exhibits an asymmetric configuration. The transition between these two limiting scenarios is governed by a third branch of solutions that is characterized by a rapid decrease of the pressure drop. Notably, across the transition the energetic gap between the symmetric and asymmetric states scales as $\delta E\sim {\mathrm{\Delta }}^2$. Therefore, in the limit $\mathrm{\Delta }\ll 1$ small variations in the energy are accompanied by relatively large changes in the elastic shape.

The fiber Bragg grating (FBG) may be viewed as a one dimensional photonic band-gap crystal by virtue of the periodic spatial perturbation imposed on the fiber core dielectric material. Similar to media supporting Bloch waves, the engraved weak index modulation, presenting a periodic “potential” to an incoming guided mode photon of the fiber, yields useful spectral properties that have been the basis for sensing applications and emerging quantum squeezing and solitons. The response of an FBG sensor to arbitrary external stimuli represents a multiphysics problem without a known analytical solution despite the growing use of FBGs in classical and quantum sensing and metrology. Here, we study this problem by first presenting a solid mechanics model for the thermal and elastic states of a stratified material. The model considers an embedded optical material domain that represents the Bragg grating, here in the form of an FBG. Using the output of this model, we then compute the optical modes and their temperature- and stress-induced behavior. The developed model is applicable to media of arbitrary shape and composition, including soft matter and materials with nonlinear elasticity and geometric nonlinearity. Finally, we employ the computed surface stress and temperature distributions along the grating to analytically calculate the Bragg shift, which is found to be in reasonable agreement with our experimental measurements.

The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of $N$ interacting qubits and analyze how a single-qubit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph.

Cells can sense and process various signals. Noise is inevitable in the cell signaling system. In a bacterial community, the mutual conversion between normal cells and persistent cells forms a bidirectional phenotype switching cascade, in which either one can be used as an upstream signal and the other as a downstream signal. In order to quantitatively describe the relationship between noise and signal amplification of each phenotype, the gain-fluctuation relationship is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, it is found that the bidirectional phenotype switching can directly generate interconversion noise which is usually very small and almost negligible. In particular, the bidirectional phenotype switching can provide a global fluctuating environment, which will not only affect the values of noise and covariance, but also generate additional intrinsic noise. The additional intrinsic noise in each phenotype is the main part of the total noise and can be transmitted to the other phenotype. The transmitted noise is also a powerful supplement to the total noise. Therefore, the indirect impact of bidirectional phenotype switching is far greater than its direct impact, which may be one of the reasons why chronic infections caused by persistent cells are refractory to treat.

In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.