We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We consider a scalar model of light propagation in the medium. We employ the theory of reproducing kernel Hilbert spaces, together with regularization to recover the susceptibility of two- and three-dimensional scattering media. Numerical examples illustrate the effectiveness of the proposed reconstruction method.

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of $n$ oscillators, observed at different times, can perform an arbitrary number of analog-to-$n$-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

We consider an isothermal self-gravitating system surrounding a central body. This model can represent a galaxy or a globular cluster harboring a central black hole. It can also represent a gaseous atmosphere surrounding a protoplanet. In three dimensions, the Boltzmann-Poisson equation must be solved numerically to obtain the density profile of the gas [Chavanis et al., Phys. Rev. E 109, 014118 (2024)]. In one and two dimensions, we show that the Boltzmann-Poisson equation can be solved analytically. We obtain explicit analytical expressions of the density profile around a central body which generalize the analytical solutions found by Camm (1950) and Ostriker (1964) in the absence of a central body. Our results also have applications for self-gravitating Brownian particles (Smoluchowski-Poisson system), for the chemotaxis of bacterial populations in biology (Keller-Segel model), and for two-dimensional point vortices in hydrodynamics (Onsager's model). In the case of bacterial populations, the central body could represent a supply of “food” that attracts the bacteria (chemoattractant). In the case of two-dimensional vortices, the central body could be a central vortex.

Clathrin-mediated endocytosis is the main pathway used by eukaryotic cells to take up extracellular material, but the dominant physical mechanisms driving this process are still elusive. Recently, several high-resolution imaging techniques have been used on different cell lines to measure the geometrical properties of clathrin-coated pits over their whole lifetime. Here, we first show that the combination of all datasets with the recently introduced cooperative curvature model defines a consensus pathway, which is characterized by a flat-to-curved transition at finite area, followed by linear growth and subsequent saturation of curvature. We then apply an energetic model for the composite of the plasma membrane and clathrin coat to this consensus pathway to show that the dominant mechanism for invagination could be coat stiffening, which might originate from cooperative interactions between the different clathrin molecules and progressively drives the system toward its intrinsic curvature. Our theory predicts that two length scales determine the invagination pathway, namely the patch size at which the flat-to-curved transition occurs and the final pit radius.

I formulate the theory of three dimensional “Malthusian flocks”—i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being “born” and “dying” during their motion—whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent $z=3/2$, the “anisotropy” exponent $\zeta =3/4$, and the “roughness” exponent $\chi =-1/2$. I also give the scaling laws implied by these exponents.

Multifractality of quantum states plays an important role for understanding numerous complex phenomena observed in different branches of physics. The multifractal properties of the eigenstates allow for characterising various phase transitions. In this work, we perform a thorough analysis of the impacts of an excited-state quantum phase transition (ESQPT) on the fractal behavior of both static and dynamical wave functions in a ferromagentic spin-1 Bose-Einstein condensate. By studying the features of the fractal dimensions, we show how the multifractality of eigenstates and time evolved states are affected by the presence of ESQPT. Specifically, the underlying ESQPT leads to a strong localization effect, which in turn enables us to use it as an indicator of ESQPT. We verify the ability of the fractal dimensions to probe the occurrence of ESQPT through a detailed scaling analysis. We also discuss how the ESQPT manifests itself in the fractal dimensions of the long-time averaged state. Our findings further confirm that the multifractal analysis is a powerful tool for studying of phase transitions in quantum many-body systems and also hint an potential application of ESQPTs in the burgeoning field of state preparation engineering.

We generalize a semiclassical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach make it a viable alternative to fully numerical schemes for a variety of applications in derivatives pricing.

While classical theory of phase transitions deals with systems in which shape variation is energetically neutral, the account of rigidity can lead to the emergence of new thermodynamic features. One of them is a special type of critical points that are characteristic of phase transitions specifically in solids. We develop a general theory of such rigidity-induced critical points and illustrate the results by analyzing in detail the case of an isotropic, geometrically nonlinear solid undergoing a volumetric phase transition at zero temperature.

Coupled dynamics of camphor rotors exhibit a rich variety of transient and stationary state phenomena. Although previous attempts at modeling these dynamics have captured some of this richness, certain observed states like rotor libration remain elusive in the models. We suggest a Coulomb-Yukawa-type potential of the form $\frac{1-e^{-K{r}^n}}{r}$, with $n>2$, where $K$ is the strength of coupling between two rotors and $r$ is the distance between them. The analysis proceeds by identifying fixed points and categorizing them as trivial or nontrivial. Their eigenvalues are determined to classify them as saddles or centers while varying the distance between pivots of two rotors, $L$. Numerical results are presented to validate the analytical findings. Additionally, libration motion is visualized with the new potential and the synchronization condition is established. The libration motion is also verified experimentally.

When nodes in excitable system are stimulated, the system tends to form traveling waves or self-organized spiral waves, such as electrical signals in the heart and the spread of epidemics. Networks composed of these nodes can be influenced by higher-order interactions. We utilized the FitzHugh-Nagumo (FHN) model for nodes to construct a three-layer lattice network, incorporating higher-order interactions applicable to neuronal models. We found that higher-order interactions have a suppressive effect on spiral waves, which exhibit various dynamics such as stable rotation, drifting, and dissipation under different influences of these interactions. There exists a critical threshold at which the spiral waves transition from stable rotation to dissipation. We aim to investigate real systems, such as the brain or heart, to explore this type of excitable media and provide theoretical insights into the propagation of excitation within networks.

This paper introduces a method to estimate irreversibility in multivariate time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting as a binary classifier, thus providing a model-free, nonlinear, and multivariate analysis while requiring minimal calibration of the classifier. An additional functionality of the proposed methodology is to easily dissect the contributions to the irreversibility of subsets of variable interactions, for instance, those operating at different time scales. The pipeline is divided into three phases: trajectory encoding, Markovian order identification, and irreversibility estimation via the classifier; the latter could be refined by hypothesis testing and quantification of variable interactions' contributions to irreversibility. When applied to financial markets, our findings reveal a distinctive shift: During stable periods, irreversibility is mainly related to short-term patterns, whereas in unstable periods, these short-term patterns are disrupted, leaving only contributions from stable, long-term ones.

Contagions do not exist in isolation but in the presence of other propagating quantities, with which they may compete. Furthermore, higher-order interactions (interactions involving more than two nodes) are widely represented in real-world systems. We propose a stochastic model for susceptible-infected-recovered-susceptible (SIRS) processes competing in a simplicial complex that accommodates higher-order interactions. We also propose deterministic microscopic Markov chain (MMC) and mean-field (MF) forms of this model, which we analyze to reveal conditions for the persistence of each infection. We verify our analysis via numerical simulations, which also unveil critical mass effects, discontinuous phase transitions, and bistability. The stochastic model exhibits eight distinct classes of dependence of final state on initial conditions. All eight of these classes can be approximately reproduced with MMC, but only seven are seen under MF. The class observed in MMC and approximated in the stochastic model, but missing from MF, involves three distinct steady states for a single set of parameter values. However, in the absence of higher-order interactions MF exhibits an additional class, not observed in MMC or the stochastic model, corresponding to an infinite spectrum of steady states, in which the ratio of infection levels remains at its initial level. Both MMC and MF models can exhibit sustained oscillations in which one contagion disappears while the other tends to a limit cycle.

In this paper, we examine the interplay between the lobby size $q$ in the $q$-neighbor Ising model of opinion formation [Phys. Rev. E 92, 052105 (2015)] and the level of overlap $v$ of two fully connected graphs. Results suggest that for each lobby size $q\ge 3$, a specific level of overlap $v^{*}$ exists, which destroys initially polarized clusters of opinions. By performing Monte-Carlo simulations, backed by an analytical approach, we show that the dependence of the $v^{*}$ on the lobby size $q$ is far from trivial in the absence of temperature, showing consecutive maximum and minimum, that additionally depends on the parity of $q$. The temperature is, in general, a destructive factor; its increase leads to the collapse of polarized clusters for smaller values of $v$, and additionally brings a substantial decrease in the level of polarization. However, we show that this behavior is counterintuitively inverted for specific lobby sizes and temperature ranges.

We study the viscoelastic relaxation dynamics of scale-free copolymer networks in the generalized Gaussian structures framework. We focus on the real and imaginary components of the complex dynamic modulus $G^{*}\left(\omega \right)$: the storage and loss moduli. Our chosen scale-free network model builds distinct types of hyperbranched copolymers by a careful tuning of the construction parameters, such as $\gamma$, which controls the node connectivity, or the minimum allowed degree $K_{\min }$ and the maximum allowed degree $K_{\max }$. These parameters, together with the parameters that govern the monomer-type distribution, provide significative distinct behaviors. By only varying $\gamma$ we change the topology of the copolymers and a local maximum in the region of high frequencies or a constant slope in the intermediate frequency region become more evident. Both $K_{\min }$ and $K_{\max }$ play an important role, especially in the region of intermediate frequency domain. The ratio $\sigma$ between the friction coefficients ${\zeta }_A$ and ${\zeta }_B$ of the $A$ and $B$ beads gives birth to new features, such as, new quasiplateaus or new peaks along with a shift toward lower or higher frequencies depending on the ratio value. The ratio $\eta$ between the number of $A$ and $B$ monomers influences the size of the constant slope for intermediate frequencies and it is responsible for the symmetry of the two peaks of the loss modulus.

Self-avoiding walk (SAW) represents a linear polymer chain on a large scale, neglecting its chemical details and emphasizing the role of its conformational statistics. The role of the latter is important in the formation of agglomerates and complexes involving polymers and organic or inorganic particles, such as polymer-stabilized colloidal suspensions, microemulsions, or micellar solutions. When such particles can be adsorbed on a polymer of considerably larger dimensions than themselves, this setup may represent the chelation of heavy metal ions by polymeric chelants. We consider the SAW of the length $N$ on a cubic lattice ridden by randomly distributed obstacles of the concentration $p$ interpreted as ions. The SAW monomers can bind to the obstacles with variable binding energy $\varepsilon$ mimicking the formation of the chelation bond. Pruned-enriched Rosenbluth method (PERM) Monte Carlo (MC) algorithm is applied to simulate system behavior. We focus on several relevant properties related to the chelation efficiency and strength, as functions of the variables set $\{p,N,\varepsilon \}$. The results are interpreted in terms of conformational freedom, excluded volume effects, and loop formation for the SAW, and the tendencies being predicted are in agreement with some experimental data.

We study systems of active particles, whose perception is constrained by a vision cone, that are attracted to other particles and repelled from static obstacles. We report a novel self-trapping mechanism: active particles with nonreciprocal attraction form particle chains, which eventually become closed loops that shrink around one or many obstacles. These closed loops act as effective aggregation centers. Long-lived, self-organized closed loops require to enclose obstacles to exist. Furthermore, we find that closed loops that initially exhibit local polar order, transition to a nematic state as they absorb more particles. The unveiled mechanism corresponds to a pinning behavior that strongly hinders particle diffusion. In short, closed loops dominate the large-scale properties of active systems with nonreciprocal attraction in disordered media.

Why do milk cartons and aluminum cans crumple differently from paper? Besides distinct elasticity and plasticity, their unique geometric structures also play a role. Over the past few decades, crumpled sheets have been widely studied for their fascinating mechanical, energetic, and statistical properties. These include the power-law relationship between the volume density of crumpled balls and pressure, the ratio of bending to stretching energies, and statistics on the number and length of deformations. Since these conclusions were primarily derived from studies on flat sheets, verifying whether they can be safely applied to the 3D hollow objects we encounter daily is important. A cubical box, with its sides forming flat sheets, is an ideal subject for comparison. The crumpling properties of such boxes have been examined through molecular dynamics simulations and experiments. By systematically dismantling the sides of the box, we clarified the roles of sides, corners, and open/closed boundaries. This knowledge allowed us to identify corners as the key factor causing deviations from the crumpling properties of flat sheets. One significant difference is that the power-law relationship between compaction and pressure is missing, replaced by a bump characteristic of the buckling transition. Different types of corners are found to be equally important, whether they are sharp at a singular point (as in boxes), along a curve (as in aluminum cans), or rounded (as in balls and vehicles). Special attention has been given to explaining why the vertices on the surface of a crumpled ball do not buckle, allowing them to retain the properties of a flat sheet despite their 3D appearance.

We study bridging transitions that emerge between two sinusoidally shaped walls of amplitude $A$, wavenumber $k$, and mean separation $L$. The focus is on weakly corrugated walls to examine the properties of bridging transitions in the limit when the walls become flat. The reduction of walls roughness can be achieved in two ways which we show differ qualitatively: (i) By decreasing $k$, (i.e., by increasing the system wavelength), which induces a continuous phenomenon associated with the growth of bridging films concentrated near the system necks, with the thickness of these films diverging as $\sim k^{-2/3}$ in the limit of $k\to 0$. Simultaneously, the location of the transition approaches that of capillary condensation in an infinite planar slit of an appropriate width as $\sim k^{2/3}$; (ii) in contrast, the limit of vanishing walls roughness by reducing $A$ cannot be considered in this context, as there exists a minimal value $A_{\min }(k,L)$ of the amplitude below which bridging transition does not occur. On the other hand, for amplitudes $A>A_{\min }(k,L)$, the bridging transition always precedes global condensation in the system. These predictions, including the scaling property $A_{\min }\propto k{L}^2$, are verified numerically using density-functional theory.