Neural dynamics is often investigated with tools from bifurcation theory. However, many neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the brain or the spiking nature of signals. Noise changes the dynamics with respect to the deterministic model; in particular classical bifurcation theory cannot be applied. We formulate the stochastic neuron dynamics in the Martin-Siggia-Rose de Dominicis-Janssen (MSRDJ) formalism and present the fluctuation expansion of the effective action and the functional renormalization group (fRG) as two systematic ways to incorporate corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To formulate self-consistency equations, we derive a fundamental link between the effective action in the Onsager-Machlup (OM) formalism, which allows the study of phase transitions, and the MSRDJ effective action, which is computationally advantageous. These results in particular allow the derivation of an OM effective action for systems with non-Gaussian noise. This approach naturally leads to effective deterministic equations for the first moment of the stochastic system; they explain how nonlinearities and noise cooperate to produce memory effects. Moreover, the MSRDJ formulation yields an effective linear system that has identical power spectra and linear response. Starting from the better known loopwise approximation, we then discuss the use of the fRG as a method to obtain self-consistency beyond the mean. We present a new efficient truncation scheme for the hierarchy of flow equations for the vertex functions by adapting the Blaizot, Méndez, and Wschebor approximation from the derivative expansion to the vertex expansion. The methods are presented by means of the simplest possible example of a stochastic differential equation that has generic features of neuronal dynamics.

An important question in turbulent Rayleigh-Bénard convection (RBC) is the effectiveness of convective heat transport, which is conveniently described via the scaling of the Nusselt number ($\mathrm{Nu}$) with the Rayleigh ($\mathrm{Ra}$) and Prandtl ($\mathrm{Pr}$) numbers. In RBC experiments, the heat supplied to the bottom plate is also partly transferred by thermal radiation. This heat transport channel, acting in parallel with the convective and conductive heat transport channels, is usually considered insignificant and thus neglected. Here we present a detailed analysis of conventional far-field as well as strongly enhanced near-field radiative heat transport occurring in various RBC experiments. A careful inclusion of the radiative transport appreciably changes the $\mathrm{Nu}=\mathrm{Nu}\left(\mathrm{Ra}\right)$ scaling inferred in turbulent RBC experiments near ambient temperature utilizing gaseous nitrogen and sulfur hexafluoride as working fluids. On the other hand, neither the conventional far-field radiation nor the strongly enhanced near-field radiative heat transport appreciably affects the heat transport law deduced in cryogenic helium RBC experiments.

We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c\left(t\right)$ depending on time. We find that for $c\left(t\right)\propto t^{-\alpha }$ there is a transition at $\alpha =1/2$. When $\alpha >1/2$, the solution saturates at large times towards a nonuniversal limiting distribution. When $\alpha <1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c\left(t\right)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time-dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential. (2) An exactly solvable discretization, the log-gamma polymer model. (3) Numerical simulations.

Pioneer transcription factors are a recently defined class of transcription factors which can bind directly to nucleosomal DNA; they play a key role in gene activation in certain pathways. Here we quantify their role in the initiation of nucleosome displacement within the kinetic proofreading scenario of chromatin remodeling. The model allows one to perform remodeling efficiency comparisons for scenarios involving different types of transcription factors and remodelers as a function of their binding and unbinding rates and concentrations. Our results demonstrate a way to fine-tune the specificity of processes that modify the chromatin structure in transcriptional initiation.

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven $XYZ$ spin-$1/2$ chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous matrix product ansatz, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric ($XXZ$) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open $XYZ$ model with arbitrary boundary fields, or the eight-vertex model.

The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully understood, and current models often assume a long-range infectionlike process for the dynamics of marks, due to the polymeric nature of the chromatin fiber which allows looping between distant sites. While these existing models typically consider antagonizing marks, here we propose a qualitatively different scenario which analyses the spreading of a single mark. We define a one-dimensional stochastic model in which mark spreading/infection occurs as a long-range process whereas mark erasure/recovery is a local process, with an enhanced rate at boundaries of infected domains. In the limiting case where our model exhibits absorbing states, we find a first-order-like transition separating the marked/infected phase from the unmarked/recovered phase. This suggests that our model, in this limit, belongs to the long-range compact directed percolation universality class. The abrupt nature of the transition is retained in a more biophysically realistic situation when a basal infection/recovery rate is introduced (thereby removing absorbing states). Close to the transition there is a range of bistability where both the marked/infected and unmarked/recovered states are metastable and long lived, which provides a possible avenue for controlling fate decisions in cells. Increasing the basal infection/recovery rate, we find a second transition between a coherent (marked or unmarked) phase, and a mixed, or random, one.

Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the model problem of an elastic continuum with quadrupolar defects, at finite temperature. This problem is posed and the collective behavior of the defects is analytically investigated. Using both renormalization group and field-theoretic techniques, it is found that the model has a yielding/melting transition of spinodal type.

The identification of Hawkes-like processes can pose significant challenges. Despite substantial amounts of data, standard estimation methods show significant bias or fail to converge. To overcome these issues, we propose an alternative approach based on an expectation-maximization algorithm, which instrumentalizes the internal branching structure of the process, thus improving convergence behavior. Furthermore, we show that our method provides a tight lower bound for maximum-likelihood estimates. The approach is discussed in the context of a practical application, namely the collection of outstanding unsecured consumer debt.

To suppress secular energy drift in dissipative particle dynamics simulations with energy conservation, we introduce an additional pairwise particle dynamics that allows for a microscopic energy fluctuation while conserving the total linear momentum of the system exactly. The pairwise dynamics may be regarded as an adaptation of the thermostat in isothermal dissipative particle dynamics, but leads to microcanonical instead of canonical ensemble at equilibrium and allows for a nonuniform temperature field at a steady state. The method is also effective in suppressing secular energy drift when used in combination with reverse nonequilibrium molecular dynamics moves. All of the equilibrium and transport properties we computed were unaffected by this additional pairwise dynamics.

The functions of a living cell rely on a complex network of biochemical reactions that allow it to respond against various internal and external cues. The outcomes of these chemical reactions are often stochastic due to intrinsic and extrinsic noise leading to population heterogeneity. The majority of calculations of stochasticity in reaction networks have focused on small regulatory networks addressing the role of timescales, feedback regulations, and network topology in propagation of noise. Here we computationally investigated chemical noise in a network with democratic architecture where each node is regulated by all other nodes in the network. We studied the effects of the qualitative and quantitative nature of mutual interactions on the propagation of both intrinsic and extrinsic noise in the network. We show that an increased number of inhibitory signals lead to ultrasensitive switching of average and that leads to sharp transition of intrinsic noise. The intrinsic noise exhibits a biphasic power-law scaling with the average, and the scaling coefficients strongly correlate with the strength of inhibitory signal. The noise strength critically depends on the strength of the interactions, where negative interactions attenuate both intrinsic and extrinsic noise.

The electroconvective instability (ECI) in an electrodialysis channel under a strong electric field is studied here. The phenomenon of ECI with extreme depletion (ECI-HD) is reported; that is, the overlapping vortices cause the extreme depletion zone to propagate in the horizontal direction. Using scaling theory and direct numerical simulation, we indicate a series of features under the ECI-HD. The decrease in ion transport rate with voltage in ECI-HD is different from the enhancement in the ECI with moderate depletion (ECI-MD), which results in a unique peak in the voltage-current curve. More importantly, we reveal that the ECI is regulated by a scaling factor consisting of the electric field, hydrodynamic coupling coefficient, and Péclet number. For the ECI-HD, the scaling factor has an opposite effect on the vortex size and overlimiting current as that on the ECI-MD. The extreme depletion zone of the ECI-HD also has an uncommon diffusion self-similar dynamics. These unique scaling laws allow one to establish the quantitative bridge between the ion concentration, electric field, and vortex size by the overlimiting current.

In the presence of electron neutral collisions of a frequency $\left(\nu \right)$ of the order of $\nu \ge 0.5{\omega }_p({\omega }_p$ is the plasma frequency), the collisional effects play an adverse role in the mechanism of terahertz (THz) radiation. The present work describes an approach for the efficient emission of THz radiation with the application of an external periodic electric field in the density rippled collisional plasma wherein an additional transverse component of the current is generated that adds to the THz radiation mechanism. The THz field obtained by coupling of the lasers' field with the external field is termed as an external field induced THz (EFIT). Here, the periodic wave number of the external field enables tuning of the THz radiation and helps achieve multiple resonance conditions for the excitation of large amplitude nonlinear plasma currents.

The formation of high energy density matter occurs in inertial confinement fusion, astrophysical, and geophysical systems. In this context, it is important to couple as much energy as possible into a target while maintaining high density. A recent experimental campaign, using buried layer (or “sandwich” type) targets and the ultrahigh laser contrast Vulcan petawatt laser facility, resulted in 500 Mbar pressures in solid density plasmas (which corresponds to about $4.6\times {10}^7\mathrm{J}/\mathrm{c}{\mathrm{m}}^3$ energy density). The densities and temperatures of the generated plasma were measured based on the analysis of x-ray spectral line profiles and relative intensities.

We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time decay in the energy current correlation function, which is related to the thermal conductivity via the Green-Kubo formula. From the time decay of the current correlation, we show three qualitatively crucial results. First, the anomalous exponent in the time-decay continuously changes as a function of the index of the long-range interaction. Second, there is a regime where the current correlation diverges with increasing the system size with fixed time, and hence, the exponent of the time decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher dimensions are also considered, and we found that long-range interaction can induce the anomalous exponent even in three-dimensional systems.

A two-dimensional (2D) comb model is proposed to characterize reaction-ultraslow diffusion of tracers both in backbones ($x$ direction) and side branches ($y$ direction) of the comblike structure with two memory kernels. The memory kernels include Dirac delta, power-law, and logarithmic and inverse Mittag-Leffler (ML) functions, which can also be considered as the structural functions in the time structural derivative. Based on the comb model, ultraslow diffusion on a fractal comb structure is also investigated by considering spatial fractal geometry of the backbone volume. The mean squared displacement (MSD) and the corresponding concentration of the tracers, i.e., the solution of the comb model, are derived for reactive and conservative tracers. For a fractal structure of backbones, the derived MSDs and corresponding solutions depend on the backbone's fractal dimension. The proposed 2D comb model with different kernel functions is feasible to describe ultraslow diffusion in both the backbone and side branches of the comblike structure.

We study the interaction of optical beams of different wavelengths, described by a two-component, two-dimensional (2D) nonlocal nonlinear Schrödinger (NLS) model. Using a multiscale expansion method the NLS model is asymptotically reduced to the completely integrable 2D Mel'nikov system, the soliton solutions of which are used to construct approximate dark-bright and antidark-bright soliton solutions of the original NLS model; the latter being unique to the nonlocal NLS system with no relevant counterparts in the local case. Direct numerical simulations show that, for sufficiently small amplitudes, both these types of soliton stripes do exist and propagate undistorted, in excellent agreement with the analytical predictions. Larger amplitude of these soliton stripes, when perturbed along the transverse direction, disintegrate either to filled vortex structures (the dark-bright solitons) or to radiation (the antidark-bright solitons).

We study conversion of thermal energy to mechanical energy and vice versa in an $\alpha$-Fermi-Pasta-Ulam-Tsingou (FPUT) chain with a spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenomenon is referred to as ballistic resonance. At large times, these mechanical vibrations decay monotonically, and therefore the well-known FPUT recurrence paradox occurring at zero temperature is eliminated at finite temperatures.

The interaction of two cavity solitons in a driven semiconductor laser above lasing threshold is investigated. We focus on the case in which the background field of the solitons is turbulent because the laser is below the injection locking point. We show that the solitons move spontaneously and either reach some equilibrium distance or merge. Different behaviors are found depending on how far from the injection locking point the laser is. The laser is modeled by a set of effective Maxwell-Bloch equations which include an equation for the macroscopic polarization that mimics the complex susceptibility of the semiconductor. In that way we avoid the emergence of an unphysical behavior of the background which instead appears when the polarization is adiabatically eliminated, which amounts to assuming infinite gain linewidth. The simulations are slow because the time scales of the different dynamical variables differ by four orders of magnitude. Yet, we show that the results of the complete set of equations can be accurately reproduced with a reduced set of equations where the polarization is adiabatically eliminated but a diffusion term is included in Maxwell equation, which accounts for the finiteness of the gain linewidth.

We present an automated procedure for the design of optimal actuation for flagellar magnetic microswimmers based on numerical optimization. Using this method, a magnetic actuation method is provided which allows these devices to swim significantly faster compared to the usual sinusoidal actuation. This leads to a novel swimming strategy which makes the swimmer perform a three-dimensional figure-eight trajectory. This shows that a faster propulsion is obtained when the swimmer is allowed to go out of plane. This approach is experimentally validated on a scaled-up flexible swimmer.