An information-theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure and in real-world brain connectivity networks.

Cytoskeletal filaments are capable of self-assembly in the absence of externally supplied chemical energy, but the rapid turnover rates essential for their biological function require a constant flux of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) hydrolysis. The same is true for two-dimensional protein assemblies employed in the formation of vesicles from cellular membranes, which rely on ATP-hydrolyzing enzymes to rapidly disassemble upon completion of the process. Recent observations suggest that the nucleolus, p granules, and other three-dimensional membraneless organelles may also demand dissipation of chemical energy to maintain their fluidity. Cooperative binding plays a crucial role in the dynamics of these higher-dimensional structures, but is absent from classic models of one-dimensional cytoskeletal assembly. In this paper, we present a thermodynamically consistent model of active regeneration with cooperative assembly, and compute the maximum turnover rate and minimum disassembly time as a function of the chemical driving force and the binding energy. We find that these driven structures resemble different equilibrium states above and below the nucleation barrier. In particular, we show that the maximal acceleration under large binding energies unites infinite-temperature local fluctuations with low-temperature nucleation kinetics.

The free energy of a weakly curved, isolated macroion embedded in a symmetric 1:1 electrolyte solution is calculated on the basis of linear Debye-Hückel theory, thereby accounting for nonelectrostatic Yukawa pair interactions between the mobile ions and of the mobile ions with the macroion surface, present in addition to the electrostatic Coulomb potential. The Yukawa interactions between anion-anion, cation-cation, and anion-cation pairs are independent from each other and serve as a model for solvent-mediated ion-specific effects. We derive expressions for the free energy of a planar surface, the spontaneous curvature, the bending stiffness, and the Gaussian modulus. It is shown that a perturbation expansion, valid if the Yukawa interactions make a small contribution to the overall free energy, yields simple analytic results that exhibit good agreement with the general free energy over the range of experimentally relevant interaction parameters.

The dielectric spectra of the twist bend nematic phase ($N_{\mathrm{TB}}$) of an achiral asymmetric bent-core liquid crystalline compound are studied for determining the various relaxation modes. Dielectric measurements are also carried out under the bias field $E$ up to 8 V/µm. Two molecular and two collective relaxation processes are observed. The orientational order parameters with respect to the local and the main directors determined using molecular modes are used to find the heliconical angle. The results also show that the order parameter with reference to the main director reverses its trend from increasing to decreasing at temperatures of a few degrees above the $N_{\mathrm{TB}}$ to $N$ transition. The collective relaxation modes are assigned to (a) distortions of the local director by the electric field at a frequency of $\sim 100\mathrm{kHz}$ while the periodic helical structure remains unaltered (mode attributed to flexoelectricity); (b) changes in the periodic structure arising from a coupling of the dielectric anisotropy with the electric field at the lowest frequency in the range of 100 Hz–10 kHz. Frequency of the higher frequency collective mode ($\sim 100\mathrm{kHz}$) depends primarily on the heliconical angle and has anomalous softeninglike behavior at the $N\text{−}{N}_{\mathrm{TB}}$ transition. The lowest frequency mode is studied under the bias field $E$; the modulus of the wave vector gradually vanishes on increasing $E$ (except for an initial behavior, $E^2<0.1{\mathrm{V}}^2/\mu {\mathrm{m}}^2$, which is just the opposite). The transition from the twist bend to splay bend structure is observed by a sudden drop in the frequency of this mode, followed by a linear decrease in frequency by increasing $E$. The results agree with the predictions made from the currently proposed models for a periodically distorted $N_{\mathrm{TB}}$ phase.

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the complex behavior: the first, called partial inference, requires continued knowledge of partial time-series data during the inference as well as past time-series data, while the second, called full inference, requires only past time-series data as training data. For the first case, we are able to infer long-time motion of microscopic fluid variables. For the second case, we show that the reservoir dynamics constructed from only past data of energy functions can infer the future behavior of energy functions and reproduce the energy spectrum. It is also shown that we can infer time-series data from only one measurement by using the delay coordinates. This implies that the obtained reservoir systems constructed without the knowledge of microscopic data are equivalent to the dynamical systems describing the macroscopic behavior of energy functions.

Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian “hot colloids,” the breakdown of detailed balance yields a continuous production of entropy at steady state, even for an ideal active gas. We quantify the irreversibility for a noninteracting active particle in two dimensions by treating both conjugated and time-reversed dynamics. By starting with underdamped dynamics, we identify a hidden rate of entropy production required to maintain persistence and prevent the rapidly relaxing momenta from thermalizing, even in the limit of very large friction. Additionally, comparing two popular models of self-propulsion with identical dissipation on average, we find that the fluctuations and large deviations in work done are markedly different, providing thermodynamic insight into the varying extents to which macroscopically similar active matter systems may depart from equilibrium.

The dynamics of a monochromatic light beam is studied inside the oval billiard with an inner scatter circle, which can be interpreted as a cross section of a long optical fiber. The outer oval boundary acts as a perfect reflector for the light beam while the scatter circle encloses a medium with changeable refraction index. The light beam refracts when it enters inside this circle and some drastic changes in the phase space are observed. The increase of the refractive index destroys the center of stability in the phase space leading to a spread of scattered light and the islands of traps for the light propagation become more pulverized. Numerical results are presented and discussed.

In this paper we study the dynamics of a multiplex multilayer network, where each layer is composed of identical Kuramoto-Sakaguchi phase oscillators with nonlocal coupling. We focus on a three-layer multiplex network and observe a specific form of multiplex network behavior, the macroscopic chimeralike state. It is decomposed by a splitting of the layers with initially close dynamics into subgroups. The first group consists of two layers performing one type of dynamics, whereas the rest perform the other type, after the introduction of interlayer coupling. Based on an intensive computational analysis, we show that areas of macroscopic chimeralike states are observed close to the critical transition points of intralayer (microscopic) states in the parameter space. We find that this macroscopic chimeralike state is excited at weak and medium interlayer coupling strength, wherein the interlayer phase lag here plays an important role, since this is a network parameter which controls macroscopic dynamics and transforms boundaries between intralayer states. The obtained numerical results are validated analytically by considering the multiplex network dynamics using the Ott-Antonsen reduction of the governing network equations.

Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for the joint degree distribution of a network within a generating function framework, we can quantify how degree correlations affect both the onset of global cascades and the propensity of nodes of specific degree class to trigger large cascades. However, not all degree correlations are equally important in a spreading process. We introduce a new measure of degree assortativity that accounts for correlations among nodes relevant to a spreading cascade. We show that the critical point defining the onset of global cascades has a monotone relationship to this new assortativity measure. In addition, we show that the choice of nodes to seed the largest cascades is strongly affected by degree correlations. Contrary to traditional wisdom, when degree assortativity is positive, low degree nodes are more likely to generate largest cascades. Our work suggests that it may be possible to tailor spreading processes by manipulating the higher-order structure of networks.

The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Löwen [Phys. Rev. Lett. 110, 055702 (2013)] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

Results of recent large-scale molecular dynamics simulations of dislocation-mediated solid plasticity are compared with predictions of the statistical thermodynamic theory of these phenomena. These computational and theoretical analyses are in substantial agreement with each other in both their descriptions of strain-rate-dependent steady plastic flows and of transient stress peaks associated with initially small densities of dislocations. The comparisons between the numerical simulations and basic theory reveal inconsistencies in some conventional phenomenological descriptions of solid plasticity.

Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g., large molecules or spin glasses. In simulations this usually requires sampling conformational transitions or phase transitions, but efficient sampling is often difficult to attain due to the roughness of the energy landscape. For Boltzmann distributions, crossing rates decrease exponentially with free-energy barrier heights. Thus, exponential acceleration can be achieved in simulations by applying an artificial bias along $\lambda$ tuned such that a flat target distribution is obtained. A flat distribution is, however, an ambiguous concept unless a proper metric is used and is generally suboptimal. Here we propose a multidimensional Riemann metric, which takes the local diffusion into account, and redefine uniform sampling such that it is invariant under nonlinear coordinate transformations. We use the metric in combination with the accelerated weight histogram method, a free-energy calculation and sampling method, to adaptively optimize sampling toward the target distribution prescribed by the metric. We demonstrate that for complex problems, such as molecular dynamics simulations of DNA base-pair opening, sampling uniformly according to the metric, which can be calculated without significant computational overhead, improves sampling efficiency by 50%–70%.

The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a landscape comes down to obtaining the quasipotential, a scalar function that quantifies the likelihood of reaching each point in the state space. In this work we provide a novel method for constructing such landscapes by extending a tool from control theory: the sum-of-squares method for generating Lyapunov functions. Applicable to any system described by polynomials, this method provides an analytical polynomial expression for the potential landscape, in which the coefficients of the polynomial are obtained via a convex optimization problem. The resulting landscapes are based on a decomposition of the deterministic dynamics of the original system, formed in terms of the gradient of the potential and a remaining “curl” component. By satisfying the condition that the inner product of the gradient of the potential and the remaining dynamics is everywhere negative, our derived landscapes provide both upper and lower bounds on the true quasipotential; these bounds becoming tight if the decomposition is orthogonal. The method is demonstrated to correctly compute the quasipotential for high-dimensional linear systems and also for a number of nonlinear examples.

Because the existence of cheap emulators can give rise to potentially drastic computational savings as compared to direct numerical simulations of complex turbulence models, the study of reduced models has good practical relevance, and the guidelines regarding their construction from the true dynamical system model are much in demand. In accordance with this contemporary trend in science and engineering, we provide a new approach for the rigorous derivation of the linear reduced model with memory from the one-dimensional Majda-McLaughlin-Tabak (MMT) prototypical wave turbulence in thermal equilibrium. The basic idea in obtaining the physics-constrained autoregressive model is to perform the discretization in time of the generalized Langevin equation (GLE) governing a single wave profile of the true dynamical system model; the GLE formalized in the Mori-Zwanzig (MZ) projection theory is the exact reduced-order equation and the closed-form rearrangement of the canonical equation of motion for the Hamiltonian system. We study the performance of the resulting linear non-Markovian model in addressing two different manners of uncertainty quantification (UQ) problems: prediction and filtering. In doing so, we perform a comparison analysis against the linear and nonlinear Markovian models describing the MMT system, which are also built upon the GLE under the MZ framework. Finally we discuss an optimal selection of the statistical model in applying the reduced-model approach to the UQ of the turbulent signal.

The spatiotemporal spectrum of feedback-driven fluctuations of brain connectivity is investigated using nonlinear neural field theory of the corticothalamic system. Weakly nonlinear dynamics of neural feedbacks are expanded in terms of first order perturbations of neural activity relative to a fixed point. Susceptibilities are used to quantify the change in connectivity per unit change in presynaptic or postsynaptic activity caused by nonlinear feedbacks such as facilitation, depression, sensitization, potentiation, and the effects of discrete eigenmode structure are included for a spherical brain geometry. Spectral signatures such as resonances are identified that allow the presence of particular presynaptic and postsynaptic feedback effects to be inferred. These include additional resonances at high frequencies and shifts of existing spectral peaks, mostly visible in the lowest spatial modes of the response.

We investigated the velocity of an asymmetric camphor boat moving on aqueous solutions with glycerol. The viscosity was controlled by using several concentrations of glycerol into the solution. The velocity decreased with an increase in the glycerol concentration. We proposed a phenomenological model, and we showed that the velocity decreased with an increase in the viscosity according to power law. Our experimental result agreed with the one obtained from our model. These results suggest that a decay length of the camphor concentration at the front side of the boat is sufficiently shorter than that of the rear side.

This paper addresses the dielectric response of a charged, oblate spheroidal particle immersed in an electrolyte. Analytic solutions are obtained for the polarization coefficient in the thin double layer limit for frequencies in the megahertz to gigahertz range. Two different distributions of the equilibrium surface charge density in the double layer are considered. The first is when the surface charge density is uniform. The second is a particular nonuniform distribution with more charges along the flat surface of the spheroid than along the edges. For this latter case, an exact solution for the polarization coefficients is obtained. In these solutions for the polarization coefficients, to a good approximation, the particles act as if they have conductivity in addition to permittivity, with different values for the conductivity depending on whether the applied electric field is parallel or perpendicular to the flat surface of the particle. When it is parallel to the flat surface, the apparent conductivity of the particle is roughly proportional to total charge on the particle and, hence, does not appear to depend on the details of the surface charge density. When the electric field is perpendicular to the flat surface, the apparent conductivity decreases as the particle becomes more platy and as the charge along the edges decreases. The effect on the dielectric dispersion of a dilute mixture of these charged spheroids in an electrolyte is also calculated. When their symmetry axes are aligned parallel to the applied electric field, the charges on the spheroids reduce the dielectric dispersion, while for spheroids aligned in the other direction, the charges increase both the conductivity and the dielectric dispersion.

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long timescales, while the interval between successive crossings on short timescales shows a power-law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.

Point-vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the stream function. Special focus is given to the case of the surface quasigeostrophic (SQG) equations, for which the existence of finite-time singularities is still a matter of debate. Point-vortex trajectories are expressed using Nambu dynamics. The formulation is based on a noncanonical bracket and allows for a geometrical interpretation of trajectories as intersections of level sets of the Hamiltonian and Casimir. Within this setting, we focus on the collapse of solutions for the three-point-vortex model. In particular, we show that for SQG the collapse can be either self-similar or non-self-similar. Self-similarity occurs only when the Hamiltonian is zero, while non-self-similarity appears for nonzero values of the same. For both cases, collapse is allowed for any choice of circulations within a permitted interval. These results differ strikingly from the classical point-vortex model, where collapse is self-similar for any value of the Hamiltonian, but the vortex circulations must satisfy a strict relationship. Results may also shed a light on the formation of singularities in the SQG partial differential equations, where the singularity is thought to be reached only in a self-similar way.

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for high dimensional systems due to practical limitations. However the network dynamics might be observable from a reduced set of measured variables but how to reliably identify the minimum set of variables providing full observability still remains an unsolved problem. In order to tackle this issue from the Jacobian matrix of the governing equations, we construct a pruned fluence graph in which the nodes are the state variables and the links represent only the linear dynamical interdependences after having ignored the nonlinear ones. From this graph, we identify the largest connected subgraphs with no outgoing links in which every node can be reached from any other node in the subgraph. In each one of them, at least one node must be measured to correctly monitor the state of the system in a $d$-dimensional reconstructed space. Our procedure is here tested by investigating large-dimensional reaction networks. Our results are validated by comparing them with the determinant of the observability matrix which provides a rigorous assessment of the system's observability.