Many biophysical processes begin when the fastest searcher finds a target out of many random searchers, which is called an extreme or fastest first passage time (fFPT). In some models (i) the fFPT vanishes logarithmically as the number of searchers grows and (ii) the fFPT can be faster for subdiffusive search compared to normal diffusion. Though mathematically rigorous, the relevance of (i) and (ii) to actual physical systems is suspect since their derivations involve searchers which move with unbounded speed. Indeed, we previously proved that the fFPT for searchers with bounded speed converges exponentially to a strictly positive minimal search time as the number of searchers grows. In this paper we study fFPTs for a broad class of anomalous and normal diffusion models with bounded or unbounded speed. These models include scaled Brownian motion, Riemann-Liouville fractional Brownian motion, and fractional Brownian motion. For all of these models, we show that the fFPT decays logarithmically in the number of searchers and that subdiffusion can be faster than normal diffusion (we further show that superdiffusion can be slower than normal diffusion). In this sense features (i) and (ii) are rather universal. On the other hand, we show that the parameter regimes in which (i) and (ii) are valid depend on the particulars of the individual model, and thus ambiguities remain in the relevance of these features to specific physical systems.
Inspired by motile cells in tissue formation, we find that active systems of self-aligning adhesive particles undergo ballistic aggregation through a flocking transition. This kinetic regime emerges when the cluster persistence length grows faster with cluster mass than the intercluster distance does. We also identify and explain distinct noncollective kinetic regimes, including biologically relevant long-lived transients. Our analytical and numerical results offer a framework explaining the broad range of experimentally observed aggregation exponents in cellular systems and reveal physical principles potentially critical for timely tissue organization.
Chains of 1000 granules in mutual contact, without precompression, and with random radii that follow a normal distribution are studied numerically. The standard deviation σ controls the disorder level. The chains are subject to (i) a striker impact and (ii) an actuator that imposes band-limited white-noise motion at one boundary. For striker excitation, a critical σ_{c}≈0.1 separates weak and strong disorder, and the propagation of the median peak momentum exhibits two regimes: (i) for short distances, a σ-dependent decay, and (ii), at long distances, a universal power law ∝k^{-0.83}, where k denotes the granule position. For actuator excitation, the transfer function reveals a transition from a low-pass response, at σ<0.3, to broadband mechanical noise suppression for higher disorder levels. The narrow passbands at a few hundred hertz that we observe are consistent with the preferred transmission bands in soils reported experimentally in the literature. Thus, simple disordered granular chains provide a minimal model to investigate selective transmission or attenuation in random granular media. The findings are relevant to near-surface site characterization, shallow buried-object detection, and related geophysical applications.
We derive the asymptotic behavior of the radial distribution function g(x) for one-dimensional (1D) hard-rod systems and related quasi-one-dimensional geometries at high packing fractions using Laplace transform techniques and pole analysis. By identifying the poles and residues of the Laplace transform in the limit of small void fraction, we obtain compact representations of g(x) in terms of the Jacobi elliptic theta function θ_{3}. This formulation naturally captures the two regimes governing the oscillatory decay toward unity: an intermediate algebraic decay and a long-distance exponential decay, consistent with previous results for the Tonks gas. Our approach provides a unified framework that (i) expresses g(x) in a single well-tabulated special function, (ii) links spatial correlations directly to the pole structure in complex Laplace space, offering clear physical insight into decay rates and oscillation frequencies, and (iii) generalizes straightforwardly to 1D binary mixtures and confined hard-disk systems, where direct Gaussian decompositions are cumbersome. The equivalence between the theta-function representation and the Gaussian superposition of [L. Bouzar et al., Phys. Rev. E 112, L042105 (2025)2470-004510.1103/bjbt-61d9] is established via the Poisson summation formula, highlighting the versatility and conceptual advantages of the Laplace-pole framework.
Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using extensive Monte Carlo off-lattice simulations of a simple structure-based model, we isolate the effect of topology by comparing simulations that preserve the linear topology of the chain with simulations that allow chain crossings. This controlled framework enables us to isolate topological effects from sequence, structure, and energetic contributions. We show that protein kinetic stability, defined as resistance to unfolding at a fixed temperature, is higher in knotted proteins. Additionally, kinetic stability increases significantly with knot depth, whereas foldability (or folding efficiency) is comparatively less affected. By considering a simple model of protein evolution in which amino-acid alphabet size is used as a proxy for evolutionary time, we find that increasing primary-sequence complexity through the addition of biotic amino acids predominantly enhances kinetic stability. Taken together, these results indicate that kinetic stability is a functional advantage conferred by protein knots and suggest that evolutionary pressure for kinetic stability could contribute to the persistence of knotted proteins.
We investigated the local dynamics of polybutadiene over a wide temperature range, from the glassy state to the liquid (rubbery) state, using quasielastic neutron scattering (QENS) combined in a recently developed modified mode distribution analysis. This approach enabled high-precision separation of QENS spectra into vibrational components and multiple relaxation processes without relying on specific model functions. Among these processes, the subpicosecond fast process was analyzed using a local diffusion model, which characterizes the dynamics via two physically meaningful parameters: the local diffusion coefficient and the harmonic potential stiffness. Temperature-dependent analysis revealed a distinct dynamic transition near the glass transition, which is interpreted as the disappearance of cooperative diffusion involving multiple segments. Furthermore, an additional relaxation mode, termed the extra-fast process, was identified and interpreted as a higher-order mode within the local diffusion model. These findings suggest a unified physical framework for the evolution of local motions across the glass transition and establish a robust methodology for quantifying polymer dynamics at subnanometer and subpicosecond scales.
Allosteric regulation in proteins arises from collective dynamics distributed over networks of residue contacts, but how multiple communication pathways contribute to signal transmission and noise suppression remains unclear. Here we develop a spanning-tree-based framework to quantify allosteric communication as an ensemble of pathways in protein contact networks. We introduce a dynamic distance measure linking local perturbations of residue interactions to global changes in network entropy, establishing a local-to-global scaling between local dynamics and global sensitivity. Using spanning-tree calculus, we derive exact probabilities for all simple paths connecting prespecified functional residue pairs. This enables a comparison between an approximate description based on uniform path usage and a topology-aware description in which path probabilities are determined by the Burton-Pemantle theorem and reflect network dependencies. From these path ensembles, we define corresponding signal-to-noise ratios and quantify how pathway multiplicity and statistical weighting shape noise suppression. Applied to KRAS and to 20 additional allosteric proteins spanning diverse functional classes, the analysis shows large variability in path usage, entropy reduction, and signal-to-noise enhancement, while consistently demonstrating that topology-aware weighting concentrates signal transmission onto dominant short pathways. This suggests that the robustness of allosteric signaling is a fundamental emergent property of protein contact topology. The spanning tree ensemble constitutes a distinct physical model whose partition function is the matrix tree theorem; the Gaussian network model is recovered as its high temperature limit. These results provide a quantitative framework linking protein structure, dynamics, and information flow, and show that robustness in allosteric communication, manifested as noise suppression through pathway redundancy, can be interpreted as an intrinsic noise averaging mechanism arising from network topology.
Nanoparticle-protein dispersions constitute complex soft materials in which competing attractive and repulsive interactions can strongly influence their phase behavior, including gelation. In this work, we demonstrate a strategy to utilize interaction between anionic silica nanoparticles and anionic protein bovine serum albumin to achieve heat-induced gels with tunable physical properties. Upon heating, the protein molecules in solution undergo unfolding followed by hydrophobic aggregation, leading to the formation of a three-dimensional gel network. The introduction of negatively charged nanoparticles generates additional electrostatic repulsion that competes with the attractive hydrophobic interactions between partially unfolded proteins. This competition modifies both the structure and mechanical properties of the resulting gels. In particular, nanoparticle-protein gels exhibit markedly enhanced optical transparency (∼90%) compared with gels formed from pure protein solutions (<1%). Rheological measurements further show shear-thinning behavior, with the gel strength decreasing systematically with increasing nanoparticle concentration, leading to progressively softer gels. At sufficiently high nanoparticle content, gelation is completely suppressed, thereby stabilizing the protein dispersion against thermal aggregation. The underlying mechanism is elucidated in terms of interaction potentials obtained by modeling small-angle neutron scattering data measured in situ during gel formation. Finally, we demonstrate that nanoparticle concentration and ionic strength serve as effective parameters to control gel opacity and mechanical rigidity, enabling the formation of both soft and rigid gels. These results demonstrate how nanoparticle-mediated interactions can regulate aggregation and gelation in protein-based soft matter systems.
The instability mechanism in general reaction-diffusion-advection systems is key to understanding flow-driven self-organization. Here we report the general conditions for instability in d-dimensional space, formally termed relative advection instability (RAI) given its exclusive dependence on the relative velocity difference. We demonstrate that the critical wave vector at the onset of instability aligns with the relative advection direction, leading to emergent traveling waves, whereas stationary periodic patterns only occur under specific orientations. Unlike the classical Turing paradigm, RAI is governed by a critical advection disparity rather than a diffusion ratio, allowing for patterns even with equal diffusion coefficients. Numerical simulations confirm that these patterns consist of traveling waves with distinct wavelengths, speeds, and amplitudes.
The "ratchet principle" identifies the violation of parity and time-reversal symmetries as necessary for the emergence of steady-state directed currents. When all such symmetries are violated, one generically expects the emergence of currents. We study stochastic systems in the presence of asymmetric fluctuation sources, which violate these symmetries and yet fail to display steady currents. We show that this stems from a hidden conservation law for momentum. For underdamped and overdamped Brownian dynamics, we show that thermal fluctuations cannot power the momentum sources required to sustain directed currents, even when time-reversal symmetry is broken due to an inhomogeneous temperature field. While active Brownian and run-and-tumble particles display interaction-induced directed currents in asymmetric activity landscapes, we show that effective momentum conservation prevents this in Active Ornstein-Uhlenbeck particles: not all inhomogeneous active fluctuations can power transport. For each of the systems considered in this article, we numerically test for the emergence of interaction-induced directed currents. We then characterize time-reversal (a)symmetry in position space using a combination of path-integral and operator methods. When the existence of effective momentum conservation is ruled out, we develop perturbation theories to characterize the onset of interaction-induced directed currents.
We present an analytical model for the frequency response of a gas microbubble oscillating near a spherical inclusion of arbitrary size and mechanical nature (rigid, fluid, or viscoelastic) immersed in a viscous compressible fluid. The model considers both radial and nonspherical oscillations in the linear regime and predicts how their resonance frequencies and oscillation amplitudes are altered by the bubble size, material properties, and distance to the nearby sphere. As a key application, we demonstrate that scanning the frequency response of a bubble near a viscoelastic object, such as an erythrocyte-like particle mimicking a biological cell, offers a way to recover its mechanical properties through inverse modeling, opening new possibilities for high-resolution elastography at the microscale.
This experimental work reinvestigates the breakdown voltage in air for electrode gaps ranging from 0.10 to 6.00µm. Rarely addressed in the literature of the field, a special focus is placed on varying the gas humidity and its direct impact on the breakdown voltage. For short distances (<2µm), the results confirm significant deviations from the predictions of Paschen's law, with a linear increase of the breakdown voltage. The statistical approach of [B. Disson et al., Phys. Rev. E 112, 015202 (2025)2470-004510.1103/qqsd-kgb3] reveals breakdown characteristics in dry air (T_{dew}<-40^{∘}C) to be very analogous to the previous results obtained in argon gas. There are-at least-two competing elementary mechanisms responsible to trigger the breakdown: the electrons produced by field emission (FE-mechanism) and the Townsend avalanche (A-mechanism). Breakdowns following the FE-mechanism occur systematically around the electric field value of E_{FE}=0.86V/nm, which is very close to the value measured in argon. Unexpectedly, the gradual increase of humidity in air causes a counterintuitive evolution of the breakdown voltages. While in macroscopic discharges, water molecules in the gas are known to elevate the breakdown voltages compared to dry gas, the admixture of H_{2}O drastically reduces the breakdown voltages in microgaps, e.g., 0.86 to 0.26V/nm for dew points of T_{dew} <-40^{∘}C and 10^{∘}C, respectively. The water layers adsorbed by the surface of the electrodes as well as the formation of a Taylor cone under the effect of the high electric field are discussed. This supports the analysis to understand whether H_{2}O enhances the FE-mechanism and A-mechanism or if this is an additional contribution leading to the breakdown. More generally, this study sheds light on the crucial role of humidity in microgap breakdowns and calls into question measurements results reported in the literature where humidity conditions are not documented.
Cellular Potts model (CPM) simulations display significant variation in dynamics, structural ordering, and observed phase transitions. Such differences may emerge, at least in part, because CPM simulations are not implemented in a uniform manner, specifically in terms of the definitions of cell perimeters and cell contact lengths. These definitions can have a significant effect on cell shape, dynamics, and data reproducibility. Here we explore different implementations of edge length computation and its effects on phase transitions as a function of cellular adhesion energy in confluent monolayers. While we find that edge length definition has only a modest effect on the transition point from fluidlike to solidlike behavior, it strongly impacts the structural order and dynamics of the monolayer across regimes. Lattice-based artifacts from cell-lattice alignment and overcounting of the cell contact length limit cooperative motion and structural order and cause early dynamical arrest. Using an updated, self-consistent implementation that corrects contact length in a manner that mirrors continuum models of cell migration, we find that monolayers undergo a transition from a fluid through a transient hexatic phase into an ordered solidlike phase that retains significant cooperative motion. This cooperative, fluctuation-driven solidlike phase is unique to this updated CPM implementation. Cell shapes in such monolayers are well-behaved and adhere to the expected shape thresholds used as structural indicators in other multicellular systems, making their application and comparison to experimental systems more readily interpretable.
The idea of the evolutionarily stable state (ESS) of a population is a cornerstone of evolutionary game theory; moreover, it coincides with the game-theoretic concept of Nash equilibrium. Such a state corresponds to a strategy adopted by the population such that a rare mutant strategy cannot invade the population. In parallel, the dynamical formulation of evolutionary game theory-particularly through replicator dynamics embodying the tenet of survival of the fittest-provides a framework for modeling frequency-dependent selection over time. While it is well known that an ESS corresponds to the stable fixed point in replicator dynamics, the evolutionary game-theoretic characterization of limit cycles is unknown. Here we fill this lacuna by defining an oscillatory ESS (OESS), which we prove to be a stable limit cycle. We also determine the conditions for the existence and the phase-space locations of OESSs.
Control of transcription presides over a vast array of biological processes, including those mediated by gene regulatory circuits that exhibit multistability. Within these circuits, two- and three-gene network motifs are particularly critical to the repertoire of metabolic and developmental pathways. Theoretical models of these circuits, however, often vary parameters such as dissociation constants, transcription rates, and degradation rates without specifying precisely how these parameters are controlled biologically. In this study, we examine the role of effector molecules, which can alter the concentrations of the active transcription factors that control regulation, and are ubiquitous in regulatory processes across many biological settings. We specifically consider allosteric regulation in the context of extending the standard bistable switch to three-gene networks, and explore the rich multistable dynamics exhibited in these architectures as a function of effector concentrations. We then analyze how the dynamics evolve under various interpretations of regulatory circuit mechanics, underlying inducer activity, and perturbations thereof. Notably, the biological mechanism by which we model effector control over dual-function proteins transforms not only the phenotypic trend of dynamic tuning but also the set of available dynamic regimes. In this way, we determine key parameters and regulatory features that drive phenotypic decisions, and offer an experimentally tunable structure for encoding inducible multistable behavior arising from both single- and dual-function allosteric transcription factors.
We consider a quasi-one-dimensional (quasi-1D) system that is an optical hard-wall nanotube with axial harmonic potential. This quasi-1D system possesses a quasi-1D harmonic potential that consists of a 1D harmonic trap along the z axis and a two-dimensional box trap in the x-y plane. Within the framework of quantum statistical mechanics, we find that in a quasi-1D harmonic potential, the generalized Bose-Einstein condensation (GBEC) can be classified into the two types. The first type of GBEC (GBEC_{1}) corresponds to T_{m}<T_{c}. The second type of GBEC (GBEC_{2}) corresponds to T_{c}<T_{m}. Here, T_{c} is the critical temperature of the first-step condensation and T_{m} is the critical temperature of the second-step condensation. There is a competitive mechanism between normal Bose-Einstein condensation (NBEC) and GBEC. We shall show that the standard transition temperature T_{c} is much larger than the transition temperature T_{n} of NBEC. Therefore, the state of NBEC does not occur in a quasi-1D harmonic potential. We have proposed an analytical solution to the problem of GBEC of ideal atoms in the quasi-1D harmonic potential. The number of noncondensed atoms in the first-step condensation is characterized by a series of elliptic theta functions and the number of noncondensed atoms in the second-step condensation is characterized by a single q-digamma function. If r denotes the tube radius, then this quasi-1D system can show the quantum size effect. There is a critical tube radius r_{c}. (1) If r>r_{c}, then the mediate condensate fraction N_{m}/N=0; (2) if r>r_{c}, then the standard transition temperature T_{c}=0; (3) if r>r_{c}, then T_{m}>T_{c} and this is the state of GBEC_{2}. The results of numerical calculation of the analytical solution predict many new experimental phenomena in the GBEC of ideal atoms in the quasi-1D harmonic potential. In the thermodynamic limit, the analytical expressions of the three critical temperatures and the three condensate fractions are derived.
We establish a sharp criterion for the stability of a class of compactly supported, homogeneous, symmetric states, "minimal compact solitons" or MCS states, of the time-dependent discrete nonlinear Schrödinger equation on a multilattice, L (L-DNLS). MCS states arise for multilattices where a nearest neighbor, a Laplace-type operator on L, has a flat band. Our stability criterion is in terms of the explicit form of the nonlinearity and the projection of a distinguished vector onto the flat band eigenspace. We apply our general results to MCS states of DNLS with a power-law nonlinearity for the diamond, Kagome, and checkerboard lattices. In lattices where MCS states are unstable, we demonstrate how the variation of the nonlinearity exponent enables the stabilization of small amplitude MCS states.
Boltzmann sampling is a central component of many computational frameworks, including numerous algorithms in machine learning. Although quantum annealers have been investigated as potential fast Boltzmann samplers, their dependence on environmental noise makes precise control of the effective temperature difficult, introducing uncertainty into the sampling process. As an alternative, we propose diabatic quantum annealing-a faster, purely unitary process-as a controllable Boltzmann sampler in which the effective temperature is determined by the annealing rate. Using the ferromagnetic Ising model and the Sherrington-Kirkpatrick model as test cases, we demonstrate that this method achieves rapid and accurate sampling in the high-temperature regime.
We investigate how much bias in the initial configuration is required to drive global agreement in synchronous, deterministic majority dynamics on large random d-regular graphs. Nodes take values ±1 and update their states at each discrete time step to align with the majority of their neighbors. Using the backtracking dynamical cavity method (BDCM), we estimate the minimal fraction of initial +1 nodes required to achieve a +1 consensus in p time steps. Our analysis predicts that for d≥4 an initial global minority of +1 nodes is sufficient to quickly steer the entire system toward consensus on +1. We then investigate whether such initial conditions can be determined explicitly for a given large random regular graph. To this end, we introduce a new algorithm, which we name history-passing reinforcement (HPR), designed to find such initial configurations with a minority of +1 nodes. We find, as a main result, that the HPR algorithm finds initial configurations where the minority takes over the majority for d-regular random graphs with d≥4. The HPR algorithm outperforms standard simulated annealing-based methods but does not reach the lowest densities predicted by the BDCM. Rather, the lowest density achievable by the algorithm is near the onset of a dynamical one-step replica symmetry-breaking phase, which we estimate using a one-step replica symmetry-breaking formulation of the BDCM. While we focus on the majority dynamics and random d-regular graphs, the algorithm can be extended to other dynamical rules and classes of sparse graphs.
The outflow velocity of expanding deuterium-tritium (DT) fuel can become significant after the bangtime, approaching local ion thermal velocity when the inertial confinement fusion (ICF) hotspot surpasses the ignition threshold. Under such conditions, the conventional assumption of an isotropic target-particle velocity distribution becomes questionable and the influence of bulk fluid motion on alpha-particle transport should be examined. In this paper we derive an analytical expression of the charged-particle stopping power in plasmas with arbitrary bulk fluid motion. We then apply this formalism to alpha-particle transport in an ICF hotspot. The results suggest that incorporating the background fluid velocity into the alpha-particle transport simulation results in a greater fraction of alpha-particle energy being transferred directly to the D and T ions, with a corresponding decrease in the energy deposited to electrons. These results indicate a potentially important correction to alpha-energy deposition in the post-bangtime hotspot.