Circulating tumor cell clusters play an important role in the metastatic cascade. These clusters can acquire a migratory and more invasive phenotype, and coordinate their motion to migrate as a collective. Before such clusters can form by collectively detaching from a primary tumor, however, the cluster must first aggregate in the tumor interior. The mechanism of this cluster formation process is still poorly understood. One of the possible ways for cells to cluster is by aligning their direction of motion with their neighboring cells. This work aims to investigate the role of this cell-cell alignment interaction on the formation of motile cell clusters inside the bulk of a tumor using computer simulations. We employ a cellular Potts model in which we model a two-dimensional heterogeneous confluent layer containing both motile and nonmotile cells. Our results indicate that the degree of clustering is governed by two distinct processes: the formation of clusters due to the presence of cell-cell alignment interactions among motile cells, and the suppression of clustering due to the presence of the dynamic cellular environment (comprising the nonmotile cells). We find that the largest motile clusters are formed for intermediate alignment strengths, contrary to what is observed for motile cells in free space (that is, unimpeded by a dense cellular environment), in which case stronger cell-cell alignment always leads to larger clustering. Our findings suggest that the presence of a densely packed cellular environment and strong cell-cell alignment inhibits the formation of large migratory clusters within the primary tumor, providing physical insight into potential factors at play during the early stages of metastasis.

This paper reports on the use of coherent microwave scattering (CMS) for spatially resolved electron number density measurements of elongated plasma structures induced at mid-IR femtosecond filamentation in air. The presented studies comprise one-dimensional mapping of laser filaments induced via 3.9 µm, 127.3 fs laser pulses at output energies up to 15 mJ. The axial electron number density was measured to be invariant (about $2\times {10}^{15}\mathrm{c}{\mathrm{m}}^{-3}$) along the entire filament length and for all tested laser pulse energies 5–15 mJ, and the corresponding laser intensity in the middle portion of the filament was estimated to be nearly constant for 5–15 mJ pulse energies (about $30-40\mathrm{TW}/\mathrm{c}{\mathrm{m}}^2$). These findings support that intensity clamping conditions were achieved in the experiments. The proposed approach enables capabilities that are currently unavailable to perform absolute and longitudinally resolved measurements of electron number density in laser filaments and to precisely characterize conditions associated with self-focusing and intensity clamping.

The imperfect narrow escape problem considers the mean first passage time (MFPT) of a Brownian particle through one of several small, partially reactive traps on an otherwise reflecting boundary within a confining domain. Mathematically, this problem is equivalent to Poisson's equation with mixed Neumann-Robin boundary conditions. Here, we obtain this MFPT in general three-dimensional domains by using strong localized perturbation theory in the small trap limit. These leading-order results involve factors, which are analogous to electrostatic capacitances, and we use Brownian local time theory and kinetic Monte Carlo (KMC) algorithms to rapidly compute these factors. Furthermore, we use a heuristic approximation of such a capacitance to obtain a simple, approximate MFPT, which is valid for any trap reactivity. In addition, we develop KMC algorithms to efficiently simulate the full problem and find excellent agreement with our asymptotic approximations.

Models for viral populations with high replication error rates (such as RNA viruses) rely on the quasispecies concept, in which mutational pressure beyond the so-called “error threshold” leads to a loss of essential genetic information and population collapse, an effect known as the “error catastrophe.” We explain how crossing this threshold, as a result of increasing mutation rates, can be understood as a second-order phase transition, even in the presence of lethal mutations. In particular, we show that, in fitness landscapes with a single peak, this collapse is equivalent to a ferroparamagnetic transition, where the back-mutation rate plays the role of the external magnetic field. We then generalize this framework to rugged fitness landscapes, like the ones that arise from epistatic interactions, and provide numerical evidence that there is a transition from a high average fitness regime to a low average fitness one, similarly to single-peaked landscapes. The onset of the transition is heralded by a sudden change in the susceptibility to variations in the mutation rate. We use insight from replica symmetry breaking mechanisms in spin glasses, in particular by considering the fluctuations of the genotype similarity distribution as the order parameter.

Inspired by studies of legislative-executive conflict in modern presidential democracies in South America, we present an agent-based statistical mechanics exploration of the collective, coordinated action of strategic political actors in the legislative chamber and the conditions that may result in premature changes in the executive officeholder, such as a president's impeachment or a motion of no confidence in a prime minister. The legislative actors are represented by information processing agents equipped with a neural network, and emit opinions about issues in the presidential agenda. We construct a Hamiltonian which is the sum of the costs for the agents to hold a specific set of political positions. We use replica methods for two types of disorder, in the space of weights and in the network of agents' interactions. We obtain the phase diagram of the model, where the control parameters may be loosely described as indices measuring the strategic legislative support, the presidential polling popularity and the volume of the presidential agenda under discussion. It shows an intermediate phase of coexistence of pro and con strategic behavior. This region is surrounded by pure phases where the strategic vote falls completely in the pro or con camps. Driven by external forces, the change of these indices may lead the system out of the coexistence region into the purely anti-executive phase, triggering a phase transition into a state opposing the executive leader and supporting their removal from office by constitutional means. We use data from Brazil, and show the presidential trajectories that led to impeachment or not during the democratic period which began in 1989. These trajectories ended in the region of the phase diagram in accordance to the president being removed or not from office.

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the past decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we derive the linear interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. We find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface-area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing a role identical to that of equilibrium systems.

It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid cells of the mammalian cortex, analog error correction codes have been observed to protect states against neural spiking noise, but their role in information processing is unclear. Here, we use these biological error correction codes to develop a universal fault-tolerant neural network that achieves reliable computation if the faultiness of each neuron lies below a sharp threshold; remarkably, we find that noisy biological neurons fall below this threshold. The discovery of a phase transition from faulty to fault-tolerant neural computation suggests a mechanism for reliable computation in the cortex and opens a path towards understanding noisy analog systems relevant to artificial intelligence and neuromorphic computing.

Nonequilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66 103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function.

In this paper, we study a simple model of a diffusive particle on a line, undergoing a stochastic resetting with rate $r$, via rescaling its current position by a factor $a$, which can be either positive or negative. For $\left|a\right|<1$, the position distribution becomes stationary at long times and we compute this limiting distribution exactly for all $\left|a\right|<1$. This symmetric distribution has a Gaussian shape near its peak at $x=0$, but decays exponentially for large $\left|x\right|$. We also studied the mean first-passage time (MFPT) $T\left(0\right)$ to a target located at a distance $L$ from the initial position (the origin) of the particle. As a function of the initial position $x$, the MFPT $T\left(x\right)$ satisfies a nonlocal second order differential equation and we have solved it explicitly for $0\le a<1$. For $-1<a\le 0$, we also solved it analytically but up to a constant factor $\kappa$ whose value can be determined independently from numerical simulations. Our results show that, for all $-1<a<1$, the MFPT $T\left(0\right)$ (starting from the origin) shows a minimum at $r=r^{*}\left(a\right)$. However, the optimized MFPT $T_{\mathrm{opt}}\left(a\right)$ turns out to be a monotonically increasing function of $a$ for $-1<a<1$. This demonstrates that, compared to the standard resetting to the origin $(a=0)$, while the positive rescaling is not beneficial for the search of a target, the negative rescaling is. Thus resetting via rescaling followed by a reflection around the origin expedites the search of a target in one dimension.

Advances in microarray and sequencing technologies have made possible the interrogation of biological processes at increasing levels of complexity. The underlying biomolecular networks contain large numbers of nodes, yet interactions within the networks are not known precisely. In the absence of accurate models, one may inquire if it is possible to find relationships between the states of such networks under external changes, and in particular, if such relationships can be model-independent. In this paper we introduce a class of such relationships. The results are based on the observation that changes to the equilibrium state of a network due to an alteration in an external input are “small” compared to the change in the input, a phenomenon we refer to as network modulation. It relies on the stability of the state. One consequence of network modulation is that response surfaces containing expression profiles of different mutants of an organism are low-dimensional linear subspaces. As an example, the expression profile of a double-knockout mutant generally lies close to the plane defined by the expression profiles of the wild-type and those of the two single-knockout mutants. This assertion is validated using experimental data from the sleep-deprivation network of Drosophila and the oxygen-deprivation network of Escherichia coli. The linearity of response surfaces is crucial in the design of a feedback control algorithm to move the underlying network from an initial state to a prespecified target state.

The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce, e.g., the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equations for a given closure and pair interaction potential.

It is well known that two permanent magnets of fixed orientation will either always repel or attract one another regardless of the distance between them. However, if one magnet is rotated at sufficient speed, a stable position at a given equilibrium distance can exist for a second free magnet. The equilibrium is produced by magnetic forces alone, which are strong enough to maintain a levitating state under gravity. We show that a stable levitation can be obtained when the rotating magnet is tilted from the rotation axis, with no offset in its position. In this regime, the levitating magnet remains centered and its spinning rate remains negligible, while its magnetic moment precesses in synchronization with the driving magnet. We provide a physical explanation of the levitation through a model relying on static dipolar interactions between the two magnets and present experimental results which validate the proposed theory.

The reptation Monte Carlo algorithm is a simple, physically motivated and efficient method for equilibrating semidilute solutions of linear polymers. Here, we propose two simple generalizations for the analog Amoeba algorithm for randomly branching chains, which allow us to efficiently deal with random trees with controlled branching activity. We analyze the rich relaxation dynamics of Amoeba algorithms and demonstrate the existence of an unexpected scaling regime for the tree relaxation. Our results suggest that the equilibration time for Amoeba algorithms scales in general like $N^2{\langle n_{\mathrm{lin}}\rangle }^{\mathrm{\Delta }}$, where $N$ denotes the number of tree nodes, $\langle n_{\mathrm{lin}}\rangle$ the mean number of linear segments the trees are composed of, and $\mathrm{\Delta }\simeq 0.4$.

We adapted the SWAP molecular dynamics algorithm for use in lattice Ising spin models. We dressed the spins with a randomly distributed length and we alternated long-range spin exchanges with conventional single spin flip Monte Carlo updates, both accepted with a stochastic rule which respects detailed balance. We show that this algorithm, when applied to the bidimensional Edwards-Anderson model, speeds up significantly the relaxation at low temperatures and manages to find ground states with high efficiency and little computational cost. The exploration of spin models should help in understanding why SWAP accelerates the evolution of particle systems and sheds light on relations between dynamics and free-energy landscapes.

Magnetic skyrmions, topologically stabilized chiral magnetic textures with particlelike properties, have so far primarily been studied statically. Here, we experimentally investigate the dynamics of skyrmion ensembles in metallic thin film conduits where they behave as quasiparticle fluids. By exploiting our access to the full trajectories of all fluid particles by means of time-resolved magneto-optical Kerr microscopy, we demonstrate that boundary conditions of skyrmion fluids can be tuned by modulation of the channel geometry. We observe as a function of channel width deviations from classical flow profiles even into the no- or partial-slip regime. Unlike conventional colloids, the skyrmion Hall effect can also introduce transversal flow asymmetries and even local motion of single skyrmions against the driving force which we explore with particle-based simulations, demonstrating the unique properties of skyrmion liquid flow that uniquely deviates from previously known behavior of other quasiparticles.

In data mining, density-based clustering, which entails classifying datapoints according to their distributions in some space, is an essential method to extract information from large datasets. With the advent of software-based radio, ionospheric radars are capable of producing unprecedentedly large datasets of plasma turbulence backscatter observations, and new automatic techniques are needed to sift through them. We present an algorithm to automatically identify and track clusters of radar echoes through time, using dbscan, a celebrated density-based clustering method for noisy point clouds. We demonstrate our algorithm's efficiency by tracking turbulent structures in the E-region ionosphere, the so-called radar aurora. Through conjugate auroral imagery, as well as in situ satellite observations, we demonstrate that the observed turbulent structures generally track the motion of auroras. What is more, the radar aurora bulk motions exhibit key qualities of auroral electric field enhancements that have previously been observed with various instruments. We present preliminary statistical results using our method, and briefly discuss the method's limitations and potential future adaptations.

Recent empirical studies have found different thermodynamic phases for collective motion in animals. However, such a thermodynamic description of human movement remains unclear. Existing studies of traffic and pedestrian flows have primarily focused on relatively high-speed mobility data, revealing only a fluidlike phase. This focus is partly because the parameter space of low-speed movement, which is governed predominantly by pairwise social interaction, remains largely uncharted. Here, we used ultrawideband radio frequency identification (UWB-RFID) technology to collect high-resolution spatiotemporal data on movements in four different classroom and playground settings. We observed two unique social phases in children's movements: a gaslike phase of free movement and a liquid-vapor coexistence phase characterized by the formation of small social groups. We also developed a simple statistical physics model that can reproduce different empirically observed phases. The proposed UWB-RFID technology can also be used to study the dynamics of active matter systems, including animal behavior, coordinating robotic swarms, and monitoring human interactions within complex systems, potentially benefiting future research in social physics.

Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by means of coupling the protein dynamics on the cell membrane to dynamics in the cytosol. Recent studies demonstrated that modeling the cytosolic dynamics in terms of an averaged protein pool disregards possibly crucial aspects of the pattern formation, most importantly concentration gradients normal to the membrane. At the same time, the coupling of two domains (surface and volume) with different dimensions renders many standard tools for the numerical analysis of self-organizing systems inefficient. Here, we present a generic framework for projecting the cytosolic dynamics onto the lower-dimensional surface that respects the influence of cytosolic concentration gradients in static and evolving geometries. This method uses a priori physical information about the system to approximate the cytosolic dynamics by a small number of dominant characteristic concentration profiles (basis), akin to basis transformations of finite element methods. As a proof of concept, we apply our framework to a toy model for volume-dependent interrupted coarsening, evaluate the accuracy of the results for various basis choices, and discuss the optimal basis choice for biologically relevant systems. Our analysis presents an efficient yet accurate method for analyzing pattern formation with surface-volume coupling in evolving geometries.

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the nonuniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $\mathcal{O}(NlogN)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N={10}^9$) and $3d$ ($N>{10}^7$) and demonstrate the flexibility of the approach by generating structures with designed spectral features at scale. By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level and show that stealthy hyperuniform structures generically display transmission gaps, providing a concrete example of fine-tuning of a physical property. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties nearly identical to those of simple hard spheres. Finally, we demonstrate generalizations of the approach to impose features in either continuous or discrete real space, using constraints in either continuous or discrete reciprocal space. In particular, enforcing large spectral power at peaks with the right symmetry leads to the nondeterministic generation of quasicrystalline structures in $2d$ and $3d$. This technique should become an essential tool to embed, and understand the role of, long-range correlations in disordered metamaterials.