It has been known for several decades that the third moment of the multifractal spectrum of the harmonic measure for diffusion-limited aggregates is linked to the underlying fractal dimension of the cluster. We demonstrate, using an argument based on the Hastings-Levitov formulation of diffusion-limited aggregation (DLA) in two dimensions, an even stronger link, connecting the universal amplitude of the third moment to the cluster fractal dimension. This argument can be used for both the standard circular DLA as well as DLA in a cylinder (i.e., with periodic boundary conditions); in the latter case, the relationship of the amplitude to the fractal dimension is weaker, and must be extracted via a scaling analysis.

The generalized Lotka-Volterra (GLV) framework, recently advanced by dynamical mean-field theory, enables the systematic analysis of large ecological networks. When combined with structured interaction topologies, previous studies have shown that the viability of species, defined by having a positive stationary abundance, depends on the number of their interacting neighbors or the “degree.” While such model studies usually assume that interaction strengths follow an identical distribution across all connected pairs, real ecological communities often exhibit correlations between interaction strength and a species' degree. To capture this overlooked feature, we introduce degree-dependent interaction strengths into a generalized random LV model. We identify two distinct regimes: a hub-favored phase, where highly connected species survive preferentially, and a hub-suppressed phase, where they face higher extinction risks. We analytically derive the phase boundary where these degree-dependent strengths precisely balance the connectivity effect, leaving all species equally susceptible. Crucially, these phases induce opposing shifts in the degree-degree correlation or “assortativity” of the network of viable species: the hub-favored phase enhances disassortativity by selectively removing the interactions between low-degree species, whereas the hub-suppressed phase reduces it as the interactions involving hub species tend to disappear. Ultimately, our findings demonstrate that degree-dependent interactions are a fundamental mechanism not only for shaping species survival, but for naturally reproducing the wide range of assortativity values observed in real ecological networks.

In regimes where inertia is negligible, the temporal evolution is governed by overdamped dynamics. This limit is particularly relevant in soft-matter contexts, such as polymers, colloidal suspensions, and processes occurring at the cellular scale. Being able to manipulate the dynamics of such many-particle systems would enable control over rate-dependent elastic responses, time-dependent material properties, relaxation processes, and perhaps the hydrodynamics of suspensions. In this work, we develop a framework for manipulating overdamped dynamics through local, physically motivated update rules. Our approach is inspired by ideas from physical learning and directed aging, in which microscopic parameters adapt autonomously to endow a material with a desired function. Using the Rayleighian formulation, whose minimization reproduces the overdamped equations of motion, we derive approximate directed-aging and contrastive rules tailored to dissipative systems. To demonstrate these ideas, we study a disordered Maxwell material that behaves elastically at short times but flows at long times. By locally modifying the viscous damping, we show that one can tune the viscous Poisson's ratio and shape local mechanical responses. These results illustrate how materials can be trained to exhibit targeted rate-dependent elastic and viscous behaviors.

Under molecular-scale confinement, water exhibits pronounced layered structures accompanied by periodic solid-liquid phase transitions as the channel height $h$ varies. However, the influence of temperature on such periodic phase behavior still remains poorly understood. In this work, we employed extensive molecular dynamics simulations to investigate how temperature (200–400 K) modulates these periodic transitions at medium ($1.0\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$) and high ($1.4\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$) densities with $h$ ranging from $7–15\AA$. We reveal that, compared to ambient temperature, low temperatures enable the formation of multiple ice structures, including trilayer puckered ice, bilayer square-tube ice, and bilayer mixed hexagonal ice. These ice structures are exhaustively characterized through multiple physical quantities (potential energy, diffusion coefficient, lateral pressure), density profiles, lateral radial distribution functions, hydrogen bond distributions and two-dimensional structure factors. By constructing previously unreported $T\text{−}h$ phase diagrams at medium- and high-density respectively, we determine that low temperatures can generate, stabilize, and expand ice phase regions by introducing the aforementioned ice structures, without altering the periodic phase transition pattern. Under high temperature impacts, we surprisingly find that the monolayer and bilayer ice regions at high-density can extend up to 400 K, with minimal loss of ice-phase regions. We attribute this to the fact that the strong confinement effect far outweighs thermal destabilization.

We study first-order condensation in finite open wedges using classical density functional theory (DFT) and compare the resulting microscopic phase behavior with recent macroscopic predictions. Two geometries are considered: a symmetric wedge formed by two identical inclined walls and an asymmetric wedge formed by a vertical and an inclined wall. The DFT calculations confirm the two condensed morphologies predicted for the symmetric wedge and the three morphologies predicted for the asymmetric wedge and their emergence depending on the wedge size, opening angle, and wall contact angle. Under partial-wetting conditions, the microscopic phase boundaries are in nearly perfect quantitative agreement with the macroscopic predictions, including reentrant changes between pinned and depinned meniscus configurations and the appearance of the semi-double-pinned state in the asymmetric wedge. Under complete-wetting conditions, the DFT phase diagrams retain the topology predicted by the macroscopic theory, but the single-pinned region is systematically enlarged. This shift is attributed to adsorbed liquid films, which reduce the effective width available to the gas and thereby increase the effective aspect ratio of the confinement.

The mechanical energy of an elastic beam separates into stretching and bending energies. This is a result for asymptotically thin beams, but it is often a surprisingly accurate approximation for thick beams, too. Here, we address this conundrum: We compute the deformations of a very thick elastic beam resulting from imposed, asymptotically small deformations of its midline to discover effective stretching and bending moduli. They soften with increasing beam thickness, but, strikingly, their ratio remains approximately constant. In this way, our calculations provide a justification for applying the picture of stretching and bending to thick elastic objects such as biological cell sheets.

We present Brownian dynamics simulations of the random walk of a dumbbell—two beads connected by a spring—in a one-dimensional periodic potential and compare our results in limiting cases to theoretical analytical equations. The relevant parameters in this system are the spring constant, the equilibrium distance of the spring (relative to the periodicity of the potential), and the amplitude of the potential. Dumbbells with equilibrium distances that are half-integer multiples of the potential periodicity and with a sufficiently large spring constant exhibit enhanced diffusion. The diffusion constant can exceed that of a single bead in the same potential landscape. In this case, the dumbbell resembles a traction elevator, with the two connected beads acting as the elevator car and counterweight: the “elevator effect.”

Front propagation in nonlinear systems is a central theme across physics and biology, yet classical diffusion-based models fail to capture finite-speed transport and directional persistence. In this work, we investigate the impact of multiplicative noise on persistent reaction random walks, focusing on velocity selection in both pushed and pulled regimes. Using nonperturbative renormalization theory, we derive effective reaction terms that reveal how fluctuations reshape the balance between growth and mortality. We predict a systematic stochastic acceleration alongside a qualitative inversion of noise effects depending on the stability parameter $a$: in strongly pushed fronts $(a\ge 0.7)$, noise reduces the recession speed by lowering the Allee threshold via a renormalized effective parameter $a_{\text{eff}}=a-s/2$. In the pulled regime $(a<0)$, an unconditional acceleration is observed, driven by a linear noise-induced growth term at the leading edge. These analytical predictions are validated by high-resolution stochastic simulations $(M=100)$ utilizing a Split-Heun scheme to strictly enforce the Stratonovich interpretation. The numerical results show clear quantitative agreement with the theory, confirming the strong predictive power of our effective framework. Crucially, because the noise corrections are strictly reactive, they remain completely decoupled from the hyperbolic transport mechanism—a structural feature that allows the noise signature to robustly persist across the hyperbolic-to-diffusive transport transition.

The accurate prediction of first-order phase transitions such as explosive death is essential for preventing irreversible dynamical collapse in complex networks. Many existing approaches struggle to scale to high-dimensional networks and to identify critical transitions driven by parameter variations. This work introduces a parameter-aware parallel reservoir computing (PPRC) framework, where control parameters serve as additional inputs into a nodewise reservoir architecture. This design enables efficient prediction of dynamics in large-scale networks and remains sensitive to parameter variations. The framework is trained using bidirectional parameter scanning data, establishing separate forward and backward parameter-aware models that effectively capture the hysteresis loop of phase transitions. We validate the PPRC framework on three representative oscillator networks with distinct network topologies, including a nearest-neighbor ring and small-world and random regular graphs. The results demonstrate that PPRC accurately identifies abrupt dynamical transitions, such as explosive amplitude death and oscillation death. Specifically, PPRC captures the associated hysteresis and reconstructs spatiotemporal patterns across the network under unseen parameters. PPRC can also accommodate unknown network connectivity through data-driven topology inference. This work presents an efficient machine learning approach for predicting abrupt transitions in complex systems.

Social pressure—the awareness of being observed by others—is a fundamental driver of prosocial behavior in human societies. Yet it is typically assumed that only direct neighbors exert vigilance pressure on an individual, despite empirical evidence that social influence persists to at least three degrees of separation. Here we show that extending the reach of social vigilance beyond direct neighbors substantially promotes cooperation. We couple a prisoner's dilemma on one layer of a multiplex network to a vigilance cascade on the other, with influence decaying geometrically with network distance. Extending vigilance to just the second circle of influence $(L=2)$ shifts the critical temptation for defection by roughly 36% in sparse Erdős-Rényi networks. Extending to four circles $(L=4)$ raises this threshold by over 50% in the same networks. Both shifts are topology dependent: the $L=1\to 2$ step alone already accounts for most of the gain in these sparse networks, whereas the pattern is more gradual in denser, hub-dominated Barabási-Albert networks, consistent with the decay coefficients of social influence reported in controlled experiments. The effect is strongest in sparse networks, requires that the vigilance and game layers be aligned, and reproduces directly on a real social network of physicians; in dense, hub-dominated networks the gain instead depends sharply on how fast influence decays with distance, switching between weak and strong cooperation as the decay rate crosses a threshold. Vigilance range and alignment act jointly: extending vigilance range promotes cooperation only where the monitoring and game structures are aligned, and neither factor alone is sufficient. Our results strongly suggest that even modest expansions of social awareness—such as those enabled by online social platforms—can substantially reshape the landscape of cooperative behavior in human populations.

We introduce a framework for immune-like protection in chemical reaction networks obeying deterministic evolution laws. We consider open networks with fixed chemostats and define proto-immunity as the capacity of such systems to preserve a prescribed minimum nonequilibrium throughput, despite the introduction of invading species and reactions. Within this setting, an invasion is harmful when added species or reactions drive the throughput below threshold. We then introduce a simple defense motif in which throughput loss increases the abundance of a defense molecule that selectively clears invaders. Three threat classes are analyzed as examples: the parasitic conversion of a functional intermediate, an invader-driven shunting of that intermediate toward waste, and the sequestration of an active species into an inactive complex. For each class, resistance is determined by the linear stability of the invader-free state, while invader persistence emerges through low-dimensional bifurcation structures. Our approach provides an analytically transparent framework that identifies dynamical ingredients by which open chemical reaction networks can preserve function and remove harmful invaders.

The space-charge-limited current density (SCLCD) for a one-dimensional vacuum diode for zero initial electron velocity, $u_0=0$, in vacuum is given by the Child-Langmuir law, $J_{\text{CL}}$. For electrons with $u_0\ne 0$ in vacuum, Jaffé modified $J_{\text{CL}}$ to obtain the SCLCD as $J_{\mathrm{Jaff}\acute{\mathrm{e}}}$. For current densities $J>J_{\mathrm{Jaff}\acute{\mathrm{e}}}$, electron reflections occur along with virtual cathode (VC) oscillations. Past studies have discussed hysteresis in diodes by sustaining these oscillations until $J=J_{\text{hys}}$, often claiming $J_{\text{hys}}\approx J_{\text{LD}}<J_{\mathrm{Jaff}\acute{\mathrm{e}}}$, where $J_{\text{LD}}$, also called the bifurcation solution, represents the steady-state current density where the electron velocity is zero at the VC. In this study, we demonstrate that $J_{\text{LD}}$ is not a valid steady-state solution since it represents a higher charge density than $J_{\mathrm{Jaff}\acute{\mathrm{e}}}$, the true SCLCD. We further demonstrate that $J_{\mathrm{Jaff}\acute{\mathrm{e}}}$ mathematically corresponds to the static bifurcation solution. Using particle-in-cell simulations across various gap distances and voltages, we demonstrate that $J_{\text{hys}}$ consistently differs from $J_{\text{LD}}$ and can be represented by a simple semiempirical relationship as a function of $J_{\mathrm{Jaff}\acute{\mathrm{e}}}/J_{\text{CL}}$.

We develop a unified theoretical-computational framework to investigate topology-mediated conformations and topology-controlled scaling in semiflexible hierarchical comb polymers. Polymer connectivity is encoded through graph-theoretic operators, while semiflexibility, excluded-volume interactions, and hydrodynamic coupling are incorporated via an effective stiffness metric, self-consistent mean-field renormalization, and a preaveraged Oseen tensor within a generalized Rouse-Zimm description. The resulting spectral formulation provides direct access to global conformational and hydrodynamic observables, including radius of gyration, hydrodynamic size, intrinsic viscosity, and scattering signatures. Across hierarchical generations, we identify an architecture-driven crossover from anisotropic, open conformations at low branching to compact, near space-filling morphologies at higher branching, accompanied by systematic compression of the relaxation spectrum. The proposed framework enables the systematic investigation of a broad range of topology-dependent conformational behavior in hierarchical comb-of-comb polymers. Comparison with coarse-grained molecular dynamics simulations demonstrates that the framework captures both connectivity-controlled and interaction-renormalized regimes. These findings provide a general and experimentally testable description of topology-dynamics coupling in complex macromolecular systems and offer a predictive basis for interpreting scattering, dynamical, and rheological responses in hierarchically branched polymers.

Quantum squeezed states are crucial for advancing precision measurement and exploring quantum optics, but their generation is constrained by the damage threshold of conventional solid-state media. We propose a new paradigm using fully ionized plasma to overcome this limitation. The method uses plasma waves to mediate four-wave mixing, generating quantum-correlated photon pairs in a two-mode squeezed state. Our model predicts that this method could ideally achieve 40 dB squeezing using ${10}^{16}{\mathrm{Wcm}}^{-2}$ pumps, with remarkable resilience to thermal noise. By circumventing material breakdown, this plasma-based platform enables squeezing at near-kW-level peak power and is scalable to shorter wavelengths, suggesting potential applications in strong-field QED and x-ray quantum optics.

Permanent particle immobilization widely emerges across complex transport systems, ranging from intracellular transport to active matter in disordered media, and constitutes a hallmark feature of such systems. Starting from the standard Lévy walk with power-law distributed flight time $\sim t^{-1-\alpha }$, we construct the immobilized Lévy walk framework by introducing a non-normalized power-law distribution to characterize flight durations for both regimes $0<\alpha <1$ and $1<\alpha <2$. In this model, particles may undergo permanent immobilization at renewal events where their flight direction is updated. By separating the particles into active and immobilized states, we derive a general propagator expression that strictly enforces probability conservation. We demonstrate that the immobilized Lévy walks obey the universal scaling $\langle x^2\left(t\right)\rangle \sim t^{2-\alpha }$, which exhibits superdiffusion for $0<\alpha <1$ and subdiffusion for $1<\alpha <2$. The system relaxes toward a power-law stationary distribution $P_{\mathrm{st}}\left(x\right)\sim {\left|x\right|}^{-1-\alpha }$, whose form matches the single-step flight length distribution. We further investigate the time-dependent propagator near the ballistic front via the infinite density formalism, an approach capable of reproducing both the asymptotic mean-squared displacement and stationary distribution. This infinite density captures key long-time statistical signatures of particle dynamics and offers fundamental insights into the dynamical impacts induced by the permanent immobilization mechanism.

Empirical evidence of scaling behaviors in neuronal avalanches suggests that neuronal populations in the brain operate near criticality. Departure from scaling in neuronal avalanches has been used as a measure of distance to criticality and linked to brain disorders. A distinct line of evidence for brain criticality has come from thermodynamic signatures in maximum entropy (ME) models. Both of these approaches have been widely applied to the analysis of neuronal data. However, the relationship between deviations from avalanche criticality and the thermodynamics of ME models of neuronal populations remains poorly understood. To address this question, we study spontaneous activity of organotypic rat cortex slice cultures in physiological and drug-induced hypo- or hyperexcitable conditions, which are classified as critical, subcritical, and supercritical based on avalanche dynamics. We find that static ME models inferred from critical cultures show signatures of criticality in thermodynamic quantities, e.g., specific heat. However, such signatures are also present and equally strong in models inferred from supercritical cultures—despite their altered dynamics and poor functional performance. On the contrary, ME models inferred from subcritical cultures do not show thermodynamic hints of criticality. Importantly, we confirm these results using an interpretable neural network model that can be tuned to and away from avalanche criticality. Our findings indicate that static maximum entropy models, although not constraining dynamical features, correctly distinguish subcritical from critical/supercritical systems. However, they may not be able to discriminate between avalanche criticality and supercriticality, suggesting that dynamics is relevant to capture the supercritical behavior and distinguish it from criticality.

We investigate composite gap solitons in a spin-orbit-coupled condensate confined in an asymmetric bichromatic superlattice with a spatially modulated nonlinearity. Although the lattice lacks exact symmetry, fundamental and dipole-type solitons retain approximate parity-symmetric profiles and remain stable over a broad portion of the first band gap. Their finite-amplitude response is examined by applying population-imbalance and relative-phase perturbations to stationary fundamental states. As the nonlinear modulation strength increases, the population-imbalance oscillations evolve continuously from compact self-trapped motion to broader oscillations about a finite mean imbalance, accompanied by a monotonic increase of the critical initial population imbalance required for self-trapping and no abrupt destabilization. The density profiles remain strongly localized throughout, with only minor shape and center-of-mass variations, indicating that the crossover is an internal reorganization. Near $V_3=1$, the single-hump state persists as the local nonlinearity weakens, while for $V_3>1$, the single-hump branch folds near $V_3\simeq 1.05$ and an independent three-hump state appears at $V_3=1.50$, remaining localized under finite perturbation. These results demonstrate composite gap solitons that remain localized under finite perturbations, with tunable internal population dynamics and a nonlinearity-controlled number of occupied lattice regions in asymmetric nonlinear superlattices.

We study the complex eigenvalue statistics of the asymmetric quantum baker map with partial projective openings. The classical asymmetric baker map, with its discontinuity at $q=2/3$, is fully chaotic, has no reflection symmetry, and provides a clean setting with tunable escape rate and fractal repeller dimension. We consider three distinct opening geometries in position space: localized (contiguous channels), random, and uniform (equispaced channels), all controlled by a tunable amplitude reflectivity parameter $\rho$ that interpolates between the fully open $(\rho =0)$ and the closed $(\rho =1)$ limits. We use the partially truncated circular unitary ensemble (PTCUE) as the random-matrix theory benchmark. The main focus is on the joint distribution of the complex spacing ratio $z$, defined as the ratio of the distances from an eigenvalue to its nearest and next-nearest neighbors in the complex plane. We find a smooth crossover from a quasi-one-dimensional spectral regime, where eigenvalues cluster near the unit circle and the phase distribution of $z$ is peaked, to a two-dimensional Ginibre-like regime, where the distribution becomes nearly uniform and level repulsion is fully developed. Both the number of open channels $M$ and the reflectivity $\rho$ modulate this crossover, and $\rho$ provides an additional continuous control even at fixed opening size. All three opening models converge to PTCUE statistics at large $M$, while differences are most pronounced for the localized model at small $M$. No evidence of an abrupt transition is found. This crossover, which suggests a universal behavior, has deep consequences for open quantum and wave-chaotic experiments.

We study the diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with cubic anharmonic potential, and analyze the recurrent behavior of its solutions. We find that two distinct types of recurrence occur. One type is the classic FPUT recurrence; for such a recurrence, we find that the relation between the recurrence period and nonlinear strength is similar to that in the monatomic case. The other type, which cannot exist in the monatomic lattice, is the recurrence due to the interactions between modes in the two branches of the dispersion relation. Indeed, we prove the existence of the optical-acoustical-acoustical resonant interaction between three Fourier modes for which a recurrent behavior in the distribution of the energy is observed. In addition, we develop a reduced Fourier-space dynamical model that reproduces the same recurrent behavior. We assess the robustness of our results through numerical simulations of the diatomic Toda lattice and the diatomic granular chain; in both cases, the same recurrent behavior is observed. Finally, in the continuous limit, we derive from the diatomic model a system of three coupled partial differential equations which are known to be integrable.