In this study, we derive semianalytical expressions for the interspike interval (ISI) distribution of model neurons driven by a two-state Markov modulated white noise. The expressions hold for a wide class of models of neurons and synapses, though not for all classes, and give an insight into the transition rate dependence of the ISI distribution. We show that by using simple and realistic model neurons. The simple one is a leaky integrate-and-fire (LIF) neuron. The realistic ones are Hodgkin-Huxley (HH) neurons with realistic synapses. For low transition rate, the transition rate dependence is essentially the same for the LIF and HH neurons. In addition, regardless of the LIF or HH neurons, as the transition rate approaches to infinity, the ISI distribution converges to the distribution of the neurons driven by the mean of the two input states. However, the speed of convergence depends on the dynamics of synapses and ion channels. Finally, we modify the expressions so that they can be applied to intrinsically bursting neurons for which the original expressions do not hold. The results in this study will be a guide to further theoretical research and useful in bridging theory and experiments.

We present a method of controlling polymorphism in self-assembly and apply it to the long-standing problem of assembly of a colloidal diamond. The latter is often viewed as the “holy grail” of the self-assembly field, due to the challenge that it presents as well as thanks to its potential as a step towards manufacturing of photonic band-gap materials. In our approach, we use a “chromatic” version of traditional building blocks, the so-called patchy particle. Namely, the individual patches that belong to the same particle in our model are distinguishable (“colored”) and their pairwise interactions are color dependent, which could be implemented with the help of DNA fictionalization. We propose a design procedure and verify it with the help of Brownian dynamics simulations. Not only are we able to “program” the self-assembly of a high-quality cubic diamond lattice, but a small modification of the coloring scheme also allows us to “reprogram” the system to assemble into the alternative polymorph, a hexagonal diamond.

A megagauss quasistatic axial magnetic field can be produced from the interaction of an intense laser beam carrying an orbital angular momentum with an underdense plasma. Three-dimensional ‘particle in cell” simulations and analytical model demonstrate that orbital angular momentum is irreversibly transferred from a tightly focused radially polarized laser beam to electrons without any dissipative effect. A theoretical model describing the individual interaction of electrons with laser shows that particles gain angular momentum during their radial and longitudinal motion in the laser field. The electron rotation and the generated axial magnetic field survive to the end of the laser-plasma interaction and continue over a long time. The agreement between particle in cell simulations and the simplified model identifies routes to increase the intensity of the solenoidal magnetic field by controlling the laser beam characteristics, such as, for example, the orbital angular momentum and/or the pulse duration.

This is an investigation of the difference between the x-ray emission of nanometer cluster targets and that of solid targets, when they are irradiated by a subrelativistic laser pulse. Special effort is made to provide comparable conditions and observables and to emphasize the specific role of target geometry. The behavior of the x-ray-emission level with respect to the laser duration shows a clear difference between target types. The x-ray duration is observed to be one order of magnitude shorter with clusters than with solid targets. The observations are reproduced by numerical simulations that corroborate the effect of the faster density and temperature decrease of clusters on the x-ray emission, as well as the ability to produce subpicosecond x-ray pulses for time-resolved applications.

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in exact diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load-balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-$1/2$ particles can be successfully determined.

We study the impact of work cost fluctuations on optimal protocols for the creation of correlations in quantum systems. We analyze several notions of work fluctuations to show that even in the simplest case of two free qubits, protocols that are optimal in their work cost (such as the one developed by Huber et al. New J. Phys. 17, 065008 (2015)) suffer work cost fluctuations that can be much larger than the work cost. We discuss the implications of this fact in the application of such protocols and suggest that, depending on the implementation, protocols that are suboptimal in their work cost could beat optimal protocols in some scenarios. This highlights the importance of assessing the dynamics of work fluctuations in quantum thermodynamic protocols.

The origin and the functions of more than a billion single-domain magnetic nanoparticles [reported in Proc. Natl. Acad. Sci. USA 89, 7683 (1992)] adjacent to billions of neurons in the brain neocortex are not known yet. There is empirical evidence implicating the sensitivity of many living organisms to constant or extremely low-frequency magnetic fields. Navigation and routing of migratory birds by the Earth's magnetic field and certain behaviors of magnetic bacteria are well-known examples. However, it seems that human beings are not able to sense the Earth's magnetic field. In this article, we first investigate the criticality of interacting magnetic superclusters in a mean-field approximation and then discuss the rotational Brownian motion of a single-domain magnetic dipole. Then, we consider the rotational Brownian motion in the presence of magnetic interactions. Ignoring the complexity of the dynamics, the anisotropy, and the long-range interaction of nanoparticles, we investigate numerically their behavior using a finite-size two-dimensional Ising-like model. It is shown that if the dipole coupling coefficient is fine-tuned to keep the model close to the critical state, then system sensitivity to an external magnetic field is maximized with an scaling behavior in terms of the number of magnetic superclusters.

In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 073211] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates ($k$-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions $g_1\left(\theta \right)$ and $g_2\left(\theta \right)$ with zero overlap and mean values ${\theta }_1$ and ${\theta }_2$, respectively; and (ii) $g_1\left(\theta \right)$ and $g_2\left(\theta \right)$ are unimodal distributions that are symmetric with respect to the middle point $({\theta }_1+{\theta }_2)/2$. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear $k$-mers on square and triangular lattices, $S$-shaped $k$-mers on square lattices and $k^2$-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.

While chimera states themselves are usually believed to be chaotic transients, the involvement of chaos behind their self-organization is not properly distinguished or studied. In this work, we demonstrate that small chimeras in the local flux dynamics of an array of magnetically coupled superconducting quantum interference devices (SQUIDs) driven by an external field are born through transiently chaotic dynamics. We deduce analytic expressions for small chimeras and synchronous states which correspond to nonchaotic attractors in the model. We also numerically study the bifurcations underlying the multistability responsible for their generation. Transient chaos manifests itself in the short-term flux oscillations with erratically fluctuating amplitudes, exponential escape time distribution, and irregular dependence of the escape time to initial conditions. We classify the small chimera states in terms of the position of the nonsynchronized member and numerically construct their basin of attraction. The basin is shown to possess an interesting structure consisting of both ordered and fractal parts, which again can be attributed to transient chaos.

A theoretical study of magnetic hyperthermia, produced by ferromagnetic particles, frozen in a carrier medium, is presented. The main emphasis of the analysis is on the effects of magnetic interaction between the particles. Any Brownian effects, including the thermally activated Néel remagnetization of the particle, are neglected. In contrast to the Néel remagnetization, the heating is the most efficient when the axes of easy magnetization of the particles are perpendicular to the field direction; magnetic interaction between the particles enhances the heat production.

The stability of a thin electrolyte film on a substrate characterized by a spatially periodic electrical charge density is considered. Using the Debye-Hückel approximation to model the electrostatic potential and the lubrication-type framework for the viscous flow description, we derive a strongly nonlinear evolution equation for the film thickness. Linear stability analysis is carried out using a combination of numerical techniques for finding the eigenvalues of the discretized stability problem, asymptotic methods valid for small charge density variation, and Floquet theory. Substrate charge nonuniformity can have either stabilizing or destabilizing effect. For the important practical case of a liquid film with boundary charge densities of opposite signs and thickness comparable to the Debye length, transition from stabilizing to destabilizing influence is observed as the patterning wavelength is decreased. A simple analytical estimate of the condition for such transition is provided. Weakly nonlinear regime is studied using analytical techniques. Numerical simulations of the strongly nonlinear evolution of the film are conducted, with emphasis on competition between patterns induced by substrate charge nonuniformity and by the intrinsic nonlinearity present even for uniformly charged substrate.

We present a numerical and theoretical investigation of the nonlinear spectral energy cascade of decaying finite-amplitude planar acoustic waves in a single-component ideal gas at standard temperature and pressure. We analyze various one-dimensional canonical flow configurations: a propagating traveling wave (TW), a standing wave (SW), and randomly initialized acoustic wave turbulence (AWT). Due to nonlinear wave propagation, energy at the large scales cascades down to smaller scales dominated by viscous dissipation, analogous to hydrodynamic turbulence. We use shock-resolved mesh-adaptive direct numerical simulation (DNS) of the fully compressible one-dimensional Navier-Stokes equations to simulate the spectral energy cascade in nonlinear acoustic waves. The simulation parameter space for the TW, SW, and AWT cases spans three orders of magnitude in initial wave pressure amplitude and dynamic viscosity, thus covering a wide range of both the spectral energy cascade and the viscous dissipation rates. The shock waves formed as a result of the energy cascade are weak $\left(M<1.4\right)$, and hence we neglect thermodynamic nonequilibrium effects such as molecular vibrational relaxation in the current study. We also derive a set of nonlinear acoustics equations truncated to second order and the corresponding perturbation energy corollary yielding the expression for a perturbation energy norm $E^{\left(2\right)}$. Its spatial average, $\langle E^{\left(2\right)}\rangle$, satisfies the definition of a Lyapunov function, correctly capturing the inviscid (or lossless) broadening of spectral energy in the initial stages of evolution—analogous to the evolution of kinetic energy during the hydrodynamic breakdown of three-dimensional coherent vorticity—resulting in the formation of smaller scales. Upon saturation of the spectral energy cascade, i.e., a fully broadened energy spectrum, the onset of viscous losses causes a monotonic decay of $\langle E^{\left(2\right)}\rangle$ in time. In this regime, the DNS results yield $\langle E^{\left(2\right)}\rangle \sim t^{-2}$ for TWs and SWs, and $\langle E^{\left(2\right)}\rangle \sim t^{-2/3}$ for AWT initialized with white noise. Using the perturbation energy corollary, we derive analytical expressions for the energy, energy flux, and dissipation rate in the wave number space. These yield the definitions of characteristic length scales such as the integral length scale $\ell$ (characteristic initial energy containing scale) and the Kolmogorov length scale $\eta$ (shock thickness scale), analogous to the K41 theory of hydrodynamic turbulence [A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 9 (1941)]. Finally, we show that the fully developed energy spectrum of the nonlinear acoustic waves scales as ${\widehat{E}}_k{k}^2{\epsilon }^{-2/3}{\ell }^{1/3}\sim Cf\left(k\eta \right)$, with $C\approx 0.075$ constant for TWs and SWs but decaying in time for AWT.

A warm plastic-shell implosion is performed on the OMEGA laser system. The measured corona plasma evolution and shell trajectory in the acceleration phase are reasonably simulated by the one-dimensional lilac simulation including the nonlocal and cross-beam energy transfer models. The results from analytical thin-shell model reproduce the time-dependent shell radius by lilac simulation and also the hot-spot x-ray-emissivity profile at stagnation predicted by spect3d. In the spect3d simulations within a clean implosion, a U-shaped hot-spot radius evolution can be observed with the Kirkpatrick-Baez microscope response (the photon energy is from 4 to 8 keV). However, a fading-away hot-spot radius evolution is measured in OMEGA warm plastic-shell implosion because of mixings. To recover the measured hot-spot x-ray emissivity profile at stagnation, a nonisobaric hot-spot model is built and the normalized hot-spot temperature, density, and pressure profiles (normalized to the corresponding target-center values) are obtained.

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a Hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks. As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology. We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding the complex behavior of real-world systems and omitting one of the approaches renders the description incomplete.

Identifying the best driver set in a complex network is an unsolved problem in the application of pinning control methods. We choose the eigenratio of the augmented Laplacian matrix, and the best driver set is the subset of nodes providing the most effective pinning control strategy, i.e., the one for which synchronization of the whole network to the reference state is attained over the widest range of the coupling parameter. In this Rapid Communication, we propose a centrality measure based on a sensitivity analysis of the Laplacian matrix of the connection graph to find an approximate solution to this problem. The proposed metric is computationally efficient as it requires only a single eigendecomposition of the Laplacian matrix. Numerical results on a number of sample networks show that the proposed metric has a significantly better accuracy than the currently used heuristics, and in most cases can correctly identify the true optimal set, which is obtainable through a combinatorial search.

The kinetic compensation effect, observed in many fields of science, is the systematic variation in the apparent magnitudes of the Arrhenius parameters, the activation energy $E_a$, and the preexponential factor $\nu$ as a response to perturbations. If, in a series of closely related activated processes, these parameters exhibit a strong linear correlation, then it is expected that an isokinetic relation will occur, and the rates assume a common value at the compensation temperature $T_c$. The reality of these two phenomena continues to be debated as they have not been explicitly demonstrated and their physical origins remain poorly understood. Using kinetic Monte Carlo simulations on a model interface, we explore how site and adsorbate interactions influence the Arrhenius parameters during a typical desorption process. We find that their transient variations result only in a partial compensation as the variations in the prefactor are not large enough to completely offset those in $E_a$. In addition, the observed isokinetic relation arises as a result of a transition to a noninteracting regime and not due to compensation between $E_a$ and $ln\nu$. These results provide a deeper insight into the microscopic events from which compensation effects and isokinetic relations originate in this system, suggesting that similar mechanisms may be at play in other systems where compensation effects have been reported.

We develop a general theory for discontinuous nonequilibrium phase transitions into an absorbing state in the presence of temporal disorder. We focus in two paradigmatic models for discontinuous transitions: the quadratic contact process (in which activation is only spread when two nearest-neighbor sites are both active) and the contact process with long-range interactions. Using simple stability arguments (supported by Monte Carlo simulations), we show that temporal disorder does not destroy the discontinuous transition in the former model. For the latter one, the first-order transition is turned into a continuous one only in the strong-disorder limit, with critical behavior belonging to the infinite-noise universality class of the contact process model. Finally, we have found that rare temporal fluctuations dramatically changes the behavior of metastable phase, turning it into a temporal Griffiths inactive phase characterized by an exponentially large decay time.

Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in the couplings. In this work we focus on stationary linear stochastic processes in continuous time and compute the transfer entropy in the presence of delay and correlated noises, using an approximate but numerically effective solution to the relevant Wiener-Hopf factorization problem. Our results rectify and complete the recent study of Barnett and Seth [L. Barnett and A. K. Seth, J. Neurosci. Methods 275, 93 (2017)].

A Lorentz gas model with rough periodic boundary conditions is proposed to investigate the boundary effect on thermal transport of noninteracting particles. The normal thermal transport is confirmed as the linear temperature gradient, and length independent thermal conductivity is obtained. We demonstrate that the thermal conductivity indeed decreases as the degree of roughness increases, which is consistent with previous works. Furthermore, we find that the thermal conductivity is oscillating with the degree of the boundary roughness. This interesting phenomenon is related to the successful transport probability of particles, which results from the interference between transporting particles and the periodic boundary conditions.

We describe a general procedure to couple two dynamical systems so as to guide their joint dynamics onto a specific transversally stable invariant submanifold in the phase space. This method can thus be viewed as a means of constraining the dynamics, with the coupling functions providing the forces of constraint, which results in the coupled systems being in generalized synchronization. The required coupling functions are, however, not uniquely defined and can therefore be chosen in order to satisfy a desired design criterion.