We present an exact solution for the height distribution of the KPZ equation at any time $t$ in a half space with flat initial condition. This is equivalent to obtaining the free-energy distribution of a polymer of length $t$ pinned at a wall at a single point. In the large $t$ limit a binding transition takes place upon increasing the attractiveness of the wall. Around the critical point we find the same statistics as in the Baik-Ben–Arous-Péché transition for outlier eigenvalues in random matrix theory. In the bound phase, we obtain the exact measure for the endpoint and the midpoint of the polymer at large time. We also unveil curious identities in distribution between partition functions in half-space and certain partition functions in full space for Brownian-type initial condition.

Self-assembly of Janus (or “patchy”) particles is dependent on the precise interaction between neighboring particles. Here, the orientations of two amphiphilic Janus spheres within a dimer in an explicit fluid are studied with high geometric resolution. Molecular dynamics simulations and semianalytical energy calculations are used with hard- and soft-sphere Lennard-Jones potentials, and temperature and hydrophobicity are varied. The most probable center-center-pole angles are in the range of ${40}^{\circ }–{55}^{\circ }$ with pole-to-pole alignment not observed due to orientational entropy. Angles near ${90}^{\circ }$ are energetically unfavored due to solvent exclusion, and the relative azimuthal angle between the spheres is affected by solvent ordering. Relatively large polar angles become more favored as the hydrophobic surface area (i.e., Janus balance) is increased.

When a magnetic nanoparticle solution flows through a porous medium formed by iron microparticles packed in a microfluidic channel, the nanoparticles get trapped within the column in the presence of a magnet. A complex interplay between magnetic and fluid forces within the magnetized porous medium governs the trapping of nanoparticles. However, how does the packing state of the microparticles affect the trapping of nanoparticles? Will more nanoparticles be trapped on a loose or a tight packing? In this work, we present experiments that show that the capture of nanoparticles is determined by the total volume occupied by the column, independent of its packing density. We present a simple analytical model based on the competition of drag and magnetic forces that shows that our system can be useful to develop and test more complete and accurate models. We also developed a technique to measure the columns' minute mass and its packing density, which consists of injecting polydimethylsiloxane into the acrylic microfluidic device. Our work can help with the optimization of environmental and biomedical applications based on high-gradient magnetic nanoparticle separation.

This study uses a simplified detonation model to investigate the behavior of detonations with galloping-like pulsations. The reactive Burgers equation is used for the hydrodynamic equation, coupled to a pulsed source whereby all the shocked reactants are simultaneously consumed at fixed time intervals. The model mimics the short periodic amplifications of the shock front followed by relatively lengthy decays seen in galloping detonations. Numerical simulations reveal a sawtooth evolution of the front velocity with a period-averaged detonation speed equal to the Chapman-Jouguet velocity. The detonation velocity exhibits two distinct groups of decay timescales, punctuated by reaction pulses. At each pulse, a rarefaction wave is created at the reaction front's last position. A characteristic investigation reveals that characteristics originating from the head of this rarefaction take 1.57 periods to reach and attenuate the detonation front, while characteristics at the tail take an additional period. The leading characteristics are amplified twice, by passing through the reaction fronts of subsequent pulses, before arriving at the shock front, while the trailing characteristics are amplified three times. This leads to the two distinct groups of timescales seen in the detonation front speed.

One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that a physics-informed deep learning framework constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from partial observations of electron pressure which is not otherwise possible using conventional equilibrium models. This technique presents a paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. The numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.

Exploiting the. broadband operating frequency regimes of a graphene flake saturable absorber (GFSA), a cavity soliton (CS) is excited in heretofore unexplored ultraviolet and visible regions. A broad-area device, namely, a vertical cavity surface emitting laser (VCSEL) is taken as a host of CSs; a two-dimensional (2D) transverse soliton, which is quite different from the conventional propagating one. The VCSEL with an embedded 2D homogeneous transverse layer of a GFSA is coupled with a frequency selective feedback. A CS is also generated in the infrared region, especially at the optical communication wavelength. Spontaneous dynamics and interaction behavior of CSs as well as generation of CS molecules and the push-broom effect are reported in this broad cross-sectional device. In comparison with other existing and potential models, the proposed VCSEL with GFSA model shows greater efficiency.

Proposed is a phenomenological modeling framework that is capable of reproducing the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), specifically the nucleation and formation of combustion pulses, the soliton-like interactions between these combustion fronts, and the fundamental, underlying Hopf bifurcation to time-periodic modulation of the waves. In this framework, the mode-locked structures are classified as autosolitons or stably propagating nonlinear waves where the local physics of nonlinearity, gain, and dissipation exactly balance. We find that the global dominant balance physics in the RDE combustion chamber are dissipative and multiscale in nature: The fast combustion physics provide the energy input to form the fundamental mode-locked autosoliton state, while the slow physics of exhaust and propellant recovery shape the waveform and dictate the number of autosolitons. In this manner, the global multiscale balance physics give rise to the stable structures—not exclusively the frontal dynamics prescribed by classical detonation theory. Experimental observations and numerical models of the RDE combustion chamber are in strong qualitative agreement. Moreover, numerical continuation (computational bifurcation tracking) of the RDE analog system indicates that a Hopf bifurcation of the steadily propagating pulse train leads to the fundamental instability of the RDE, or time-periodic modulation of the waves. Along branches of Hopf orbits in parameter space exist a continuum of wave-pair interactions that exhibit solitonic interactions of varying strength.

Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of oscillation consists of one or more large amplitude spikes followed by one or more small amplitude peaks. MMOs typically undergo period-adding bifurcations under parameter variation. We demonstrate here, in a set of three identical, linearly coupled van der Pol oscillators, a scenario in which MMOs exhibit a period-doubling sequence to chaos that preserves the MMO structure, as well as period-adding bifurcations. We characterize the chaotic nature of the MMOs and attribute their existence to a master-slave-like forcing of the inner oscillator by the outer two with a sufficient phase difference between them. Simulations of a single nonautonomous oscillator forced by two sine functions support this interpretation and suggest that the MMO period-doubling scenario may be more general.

Here we investigate the dynamics of indirect reciprocity on networks, a type of social dynamics in which the attitude of individuals, either cooperative or antagonistic, toward other individuals changes over time based upon their actions and mutual monitoring. We observe an absorbing state phase transition as we change the network's link or edge density. When the edge density is either small or large enough, opinions quickly reach an absorbing state, from which opinions never change anymore once reached. In contrast, if the edge density is in the middle range, the absorbing state is not reached and the state keeps changing, thus being active. The result shows an effect of social networks on spontaneous group formation.

Road accidents or maintenance often lead to the blockage of roads, causing severe traffic congestion. Diverted routes after road blockage are often decided individually and have no coordination. Here, we employ the cavity approach in statistical physics to obtain both analytical results and optimization algorithms to optimally divert and coordinate individual vehicle routes after road blockage. Depending on the number and the location of the blocked roads, we found that there can be a significant change in traveling path of individual vehicles, and a large increase in the average traveling distance and cost. Interestingly, traveling distance decreases but traveling cost increases for some instances of diverted traffic. By comparing networks with different topology and connectivity, we observe that the number of alternative routes plays a crucial role in suppressing the increase in traveling cost after road blockage. We tested our algorithm using the England highway network and found that coordinated diversion can suppress the increase in traveling cost by as much as $66\%$ in the scenarios studied. These results reveal the advantages brought by the optimally coordinated traffic diversion after road blockage.

Collective motion is an innate ability of all living systems, which depends on physiological and psychosocial factors in the case of humans. Such a collective organization is becoming of great interest in collective motion in human crowds. Using a cellular automaton (CA) simulation model, we demonstrate that emergency egress from a two-dimensional corridor with optimal stress leads to less evacuation time and efficient mass evacuations. We study how three types of stress (i.e., mild stress, optimal stress, and anxiety) described in the literature have a significant impact on the collective dynamics. We found that low-stress levels could decrease the evacuation time in an entire occupied room since agents choose alternative routes rather than the shortest path to the exit and display cooperative behavior. Therefore, the combination of mild and optimal stress can lead to efficient evacuations. Also CA simulations may be used to find safer and more efficient ways to conduct mass evacuation procedures.

Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We consider simple effective geometries for the spatial arrangement of cells, we calculate the mechanical work that each cell performs in order to deform the matrix, and study how that energy changes when a contracting cell is surrounded by other cells with similar properties and behavior. Cells regulating the displacements that they generate are attracted to each other in a manner that does not depend on the cell's rigidity. Whereas cells regulating the active stress that they apply repel each other. This repulsion depends on the cell's bulk modulus in spherical geometry, while in cylindrical geometries the interaction depends also on their shear modulus. In nonlinear, strain-stiffening matrices, for displacement regulation, in the presence of other cells, cell contraction is limited due to the divergence of the shear stress. For stress regulation, the interaction energy drops at the nonlinear stiffening stress. Our theoretical work provides insight into matrix-mediated interactions between contractile cells and on the role of their mechanical regulatory behavior.

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a zero-dimensional (0D; ordinary-differential-equation-level) compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations (SEAIHR model). We emphasize the importance of the viral latent period (reflected in the exposed population) and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths, the reported data we found to be most reliable, via minimizing the ${\ell }^2$ norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, and we address issues of parameter identifiability. We model both the prequarantine and postquarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model “reactions”) of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into the finite-element software package COMSOL Multiphysics$\circledR$, which was subsequently used to numerically solve the model partial differential equations. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, zero-dimensional description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.

Hand-crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by the microcomputed tomography (micro-CT) without destroying or unfolding them. From the reconstructed three-dimensional (3D) data, we examine several power laws for the crumpled square sheets of paper of the sizes $L=50$–300 mm and obtain the mass fractal dimension $D_M=2.7\pm 0.1$ by the relation between the mass and the radius of gyration of the balls and the fractal dimension $2.5\lesssim d_f\lesssim 2.8$ for the internal structure of each crumpled paper ball by the box counting method in the real space and the structure factors in the Fourier space. The data for the paper sheets are consistent with $D_M=d_f$, suggesting that the self-similarity in the structure of each crumpled ball gives rise to the similarity among the balls with different sizes. We also examine the cellophane sheets and the aluminium foils of the size $L=200$ mm and obtain $2.6\lesssim d_f\lesssim 2.8$ for both of them. The micro-CT also allows us to reconstruct 3D structure of a line drawn on the crumpled sheets of paper. The Hurst exponent for the root-mean-square displacement along the line is estimated as $H\approx 0.9$ for the length scale shorter than the scale of the radius of gyration, beyond which the line structure becomes more random with $H\sim 0.5$.

The HP model, a coarse-grained protein representation with only hydrophobic (H) and polar (P) amino acids, has already been extensively studied on the simple cubic (SC) lattice. However, this geometry severely restricts possible bond angles, and a simple improvement is to instead use the face-centered cubic (fcc) lattice. In this paper, the density of states and ground state energies are calculated for several benchmark HP sequences on the fcc lattice using the replica-exchange Wang-Landau algorithm and a powerful set of Monte Carlo trial moves. Results from the fcc lattice proteins are directly compared with those obtained from a previous lattice protein folding study with a similar methodology on the SC lattice. A thermodynamic analysis shows comparable folding behavior between the two lattice geometries, but with a greater rate of hydrophobic-core formation persisting into lower temperatures on the fcc lattice.

The gas-puff $Z$-pinch is a well-known source of x-rays and/or neutrons, but it is highly susceptible to the magneto-Rayleigh-Taylor instability (MRTI). Approaches to MRTI mitigation include density profile tailoring, in which nozzles are added or modified to alter the acceleration trajectory, and axial pre-magnetization, in which perturbations are smoothed out via magnetic field line tension. Here, we present two-dimensional magnetohydrodynamic simulations of loads driven by an 850 kA, 160 ns driver that suggest these mitigation strategies can be additive. The initial axial magnetic field, $B_{z0}$, to stabilize a 2.5-cm-radius Ne gas liner imploding onto an on-axis deuterium target can be reduced from 0.7 T to 0.3 T by adding a second liner with a radius of 1.25 cm. Because MRTI mitigation tends to increasingly lower yield with higher $B_{z0}$, the use of a lower field is advantageous. Here, we predict a reduction in yield penalty from $>100\times$ with the single liner to $<10\times$ with a double liner. A premagnetized, triple nozzle gas puff could therefore be an attractive source for intense neutrons or other fusion applications.

We present the integral decomposition for the fundamental solution of the generalized Cattaneo equation with both time derivatives smeared through convoluting them with some memory kernels. For power-law kernels $t^{-\alpha }, \alpha \in (0,1]$ this equation becomes the time fractional one governed by the Caputo derivatives in which the highest order is 2. To invert the solutions from the Fourier-Laplace domain to the space-time domain we use analytic methods based on the Efross theorem and find out that solutions looked for are represented by integral decompositions which tangle the fundamental solution of the standard Cattaneo equation with nonnegative and normalizable functions being uniquely dependent on the memory kernels. Furthermore, the use of methodology arising from the theory of complete Bernstein functions allows us to assign such constructed integral decompositions the interpretation of subordination. This fact is preserved in two limit cases built into the generalized Cattaneo equations, i.e., either the diffusion or the wave equations. We point out that applying the Efross theorem enables us to go beyond the standard approach which usually leads to the integral decompositions involving the Gaussian distribution describing the Brownian motion. Our approach clarifies puzzling situation which takes place for the power-law kernels $t^{-\alpha }$ for which the subordination based on the Brownian motion does not work if $\alpha \in (1/2,1]$.

We study the simplified Blume-Emery-Griffiths model without bilinear exchange coupling both in the microcanonical ensemble and in the canonical ensemble. This model can exhibit a zeroth-order phase transition in the microcanonical ensemble accompanied by a finite entropy jump. However, this singularity in entropy cannot be observed in the canonical ensemble, which illustrates the ensemble inequivalence. Moreover, the global phase diagram of this model is given in both ensembles.

We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyperfine spin $F=1$ ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons necessarily have a repulsive intraspecies interaction and are bound due to an attractive interspecies interaction. Due to a collapse instability in higher dimensions, an additional spin-orbit coupling is necessary to stabilize a quasi-2D symbiotic spinor soliton. Although a quasi-1D symbiotic soliton has a simple Gaussian-type density distribution, novel spatial periodic structure in density is found in quasi-2D symbiotic SO-coupled spinor solitons. For a weak SO coupling, the quasi-2D solitons are of the $(-1,0,+1)$ or $(+1,0,-1)$ type with intrinsic vorticity and multiring structure, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses are angular momenta projections in spin components $F_z=+1,0,-1$, respectively. For a strong SO coupling, stripe and superlattice solitons, respectively, with a stripe and square-lattice modulation in density, are found in addition to the multiring solitons. The stationary states were obtained by imaginary-time propagation of a mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time. The possibility of the creation of such a soliton by removing the trap of a confined spin-1 BEC in a laboratory is also demonstrated.