Shadowgraphy is a technique widely used to diagnose objects or systems in various fields in physics and engineering. In shadowgraphy, an optical beam is deflected by the object and then the intensity modulation is captured on a screen placed some distance away. However, retrieving quantitative information from the shadowgrams themselves is a challenging task because of the nonlinear nature of the process. Here, we present a method to retrieve quantitative information from shadowgrams, based on computational geometry. This process can also be applied to proton radiography for electric and magnetic field diagnosis in high-energy-density plasmas and has been benchmarked using a toroidal magnetic field as the object, among others. It is shown that the method can accurately retrieve quantitative parameters with error bars less than 10%, even when caustics are present. The method is also shown to be robust enough to process real experimental results with simple pre- and postprocessing techniques. This adds a powerful tool for research in various fields in engineering and physics for both techniques.

Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.

Numerous experiments have taken advantage of DNA as a model system to test theories for a channel-confined polymer. A tacit assumption in analyzing these data is the existence of a well-defined depletion length characterizing DNA-wall interactions such that the experimental system (a polyelectrolyte in a channel with charged walls) can be mapped to the theoretical model (a neutral polymer with hard walls). We test this assumption using pruned-enriched Rosenbluth method (PERM) simulations of a DNA-like semiflexible polymer confined in a tube. The polymer-wall interactions are modeled by augmenting a hard wall interaction with an exponentially decaying, repulsive soft potential. The free energy, mean span, and variance in the mean span obtained in the presence of a soft wall potential are compared to equivalent simulations in the absence of the soft wall potential to determine the depletion length. We find that the mean span and variance about the mean span have the same depletion length for all soft potentials we tested. In contrast, the depletion length for the confinement free energy approaches that for the mean span only when depletion length no longer depends on channel size. The results have implications for the interpretation of DNA confinement experiments under low ionic strengths.

A lattice version of the driven inelastic Maxwell gas is studied in one dimension with periodic boundary conditions. Each site $i$ of the lattice is assigned with a scalar “velocity,” $v_i$. Nearest neighbors on the lattice interact, with a rate ${\tau }_c^{-1}$, according to an inelastic collision rule. External driving, occurring with a rate ${\tau }_w^{-1}$, sustains a steady state in the system. A set of closed coupled equations for the evolution of the variance and the two-point correlation is found. Steady-state values of the variance, as well as spatial correlation functions, are calculated. It is shown exactly that the correlation function decays exponentially with distance, and the correlation length for a large system is determined. Furthermore, the spatiotemporal correlation $C(x,t)=\langle v_i\left(0\right)v_{i+x}\left(t\right)\rangle$ can also be obtained. We find that there is an interior region $-x^{*}<x<x^{*}$, where $C(x,t)$ has a time-dependent form, whereas in the exterior region $\left|x\right|>x^{*}$, the correlation function remains the same as the initial form. $C(x,t)$ exhibits second-order discontinuity at the transition points $x=\pm x^{*}$, and these transition points move away from the $x=0$ with a constant speed.

We study the thermodynamic properties of a one-dimensional gas with one-dimensional gravitational interactions. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cutoff. As a consequence, each particle carries with it its own background density. Using mean-field theory, we show that the system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Numerical simulations of the model, which include the caloric curve, the equation of state, the radial distribution function, and the largest Lyapunov exponent, confirm the existence of the phase transition, and they are in good agreement with the theoretical predictions.

Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations [belief-propagation and Thouless-Anderson Palmer (TAP) equations] in the best understood of such machines, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polarizations of neurons. In the “retrieval phase”, where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations: The set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines.

The dynamics of driven-dissipative systems is shown to be well-fitted for achieving efficient combinatorial optimization. The proposed method can be applied to solve any combinatorial optimization problem that is equivalent to minimizing an Ising Hamiltonian. Moreover, the dynamics considered can be implemented using various physical systems as it is based on generic dynamics—the normal form of the supercritical pitchfork bifurcation. The computational principle of the proposed method relies on an hybrid analog-digital representation of the binary Ising spins by considering the gradient descent of a Lyapunov function that is the sum of an analog Ising Hamiltonian and archetypal single or double-well potentials. By gradually changing the shape of the latter potentials from a single to double well shape, it can be shown that the first nonzero steady states to become stable are associated with global minima of the Ising Hamiltonian, under the approximation that all analog spins have the same amplitude. In the more general case, the heterogeneity in amplitude between analog spins induces the stabilization of local minima, which reduces the quality of solutions to combinatorial optimization problems. However, we show that the heterogeneity in amplitude can be reduced by setting the parameters of the driving signal near a regime, called the dynamic phase transition, where the analog spins' DC components map more accurately the global minima of the Ising Hamiltonian which, in turn, increases the quality of solutions found. Last, we discuss the possibility of a physical implementation of the proposed method using networks of degenerate optical parametric oscillators.

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called Voronoi cohesion which describes the probability for sharing the same Voronoi cell, when randomly choosing $g$ centers in the network. This measure provides information based on the global context (the network in its entirety), a type of information that is not carried by other similarity measures. We explore the mathematical background of this phenomenon and several of its potential applications. A special focus is laid on the possibilities and limitations pertaining to the exploitation of the phenomenon for community detection purposes.

We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges. We focus on the regime where the hidden variables follow a power law with exponent $\tau \in (2,3)$, so that the degrees have infinite variance. The natural cutoff $h_c$ characterizes the largest degrees in the hidden variable models, and a structural cutoff $h_s$ introduces negative degree correlations (disassortative mixing) due to the infinite-variance degrees. We show that local clustering decreases with the hidden variable (or degree). We also determine how the average clustering coefficient $C$ scales with the network size $N$, as a function of $h_s$ and $h_c$. For scale-free networks with exponent $2<\tau <3$ and the default choices $h_s\sim N^{1/2}$ and $h_c\sim N^{1/(\tau -1)}$ this gives $C\sim N^{2-\tau }lnN$ for the universality class at hand. We characterize the extremely slow decay of $C$ when $\tau \approx 2$ and show that for $\tau =2.1$, say, clustering starts to vanish only for networks as large as $N={10}^9$.

In this paper we derive alternative continuous time limits of the utterance selection model (USM) for language change [G. J. Baxter et al., Phys. Rev. E 73, 046118 (2006)]. This is motivated by the fact that the Fokker-Planck continuous time limit derived in the original version of the USM is only valid for a small range of parameters. We investigate the consequences of relaxing these constraints on parameters. Using the normal approximation of the multinomial approximation, we derive a continuous time limit of the USM in the form of a weak-noise stochastic differential equation. We argue that this weak noise, not captured by the Kramers-Moyal expansion, cannot be neglected. We then propose a coarse-graining procedure, which takes the form of a stochastic version of the heterogeneous mean field approximation. This approximation groups the behavior of nodes of the same degree, reducing the complexity of the problem. With the help of this approximation, we study in detail two simple families of networks: the regular networks and the star-shaped networks. The analysis reveals and quantifies a finite-size effect of the dynamics. If we increase the size of the network by keeping all the other parameters constant, we transition from a state where conventions emerge to a state where no convention emerges. Furthermore, we show that the degree of a node acts as a time scale. For heterogeneous networks such as star-shaped networks, the time scale difference can become very large, leading to a noisier behavior of highly connected nodes.

Electrons can be efficiently injected into a plasma wave by colliding two counterpropagating laser pulses in a laser wakefield acceleration. However, the generation of a high-quality electron beam with a large charge is difficult in the traditional on-axis colliding scheme due to the growth of the electron beam duration coming from the increase of the beam charge. To solve this problem, we propose an off-axis colliding scheme, in which the collision point is away from the axis of the driver pulse. We show that the electrons injected from the off-axis region are highly concentered on the tail of the bubble even for a large trapped charge, thus feeling almost the same accelerating field. As a result, quasimonoenergetic electron beams with a large charge can be produced. The validity of this scheme is confirmed by both the particle-in-cell simulations and the Hamiltonian model. Furthermore, it is shown that a Laguerre-Gauss (LG) laser can be adopted as the injection pulse to realize the off-axis colliding injection in three dimensions symmetrically, which may be useful in simplifying the technical layout of the real experiment setup.

Understanding fundamental growth processes is key to the control of nonequilibrium structure formation for a wide range of materials on all length scales, from atomic to molecular and even colloidal systems. While atomic systems are relatively well studied, molecular and colloidal growth are currently moving more into the focus. This poses the question to what extent growth laws are size scalable between different material systems. We study this question by analyzing the potential energy landscape and performing kinetic Monte Carlo simulations for three representative systems. While submonolayer (island) growth is found to be essentially scalable, we find marked differences when moving into the third (vertical) dimension.

We study a one-dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. With temperature being given, two situations are addressed: Either the colloids are kept at fixed positions (canonical ensemble) or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal. How many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left-right symmetry breakdown? We evidence a cascade of transitions as system size is varied in the canonical treatment or as pressure is increased in the isobaric formulation.

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the “flights,” that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a one-dimensional lattice, “cascades” of $n$ unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where $n$ is drawn from a cascade distribution $p_n$. We show that this local mechanism may give rise to superdiffusion or normal diffusion when $p_n$ is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two local distributions power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

The properties of the random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density ${\theta }_{\text{J}}$ and on the temporal evolution of the coverage fraction $\theta \left(t\right)$. Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit ${\theta }_{\text{J}}$. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage $\theta$ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculations suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction $\theta \left(t\right)$ to the jamming limit ${\theta }_{\text{J}}$.

Honeybees (Apis mellifera) exhibit complex coordination and interaction across multiple behaviors such as swarming. This coordination among honeybees in the same colony is remarkably similar to the concept of informational cascades. The multifractal geometry of cascades suggests that multifractal measures of individual honeybee activity might carry signatures of these colony-wide coordinations. The present work reanalyzes time stamps of entrances to and exits from the hive captured by radio-frequency identification (RFID) sensors reading RFID tags on individual bees. Indeed, both multifractal spectrum width for individual bees’ inter-reading interval series and differences of those widths from surrogates significantly predicted not just whether the individual bee's hive had a mesh enclosure but also predicted the specific membership of individual bees in one of five colonies. The significant effects of multifractality in matching honeybee activity to type of colony and, further, matching individual honeybees to their exact home colony suggests that multifractality quantifies key features of the colony-wide interactions across many scales. This relevance of multifractality to predicting colony type or colony membership adds additional credence to the cascade metaphor for colony organization. Perhaps, multifractality provides a new tool for exploring the relationship between individual organisms and larger, more complex social behaviors.

The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

Diffusion pore imaging is an extension of diffusion-weighted nuclear magnetic resonance imaging enabling the direct measurement of the shape of arbitrarily formed, closed pores by probing diffusion restrictions using the motion of spin-bearing particles. Examples of such pores comprise cells in biological tissue or oil containing cavities in porous rocks. All pores contained in the measurement volume contribute to one reconstructed image, which reduces the problem of vanishing signal at increasing resolution present in conventional magnetic resonance imaging. It has been previously experimentally demonstrated that pore imaging using a combination of a long and a narrow magnetic field gradient pulse is feasible. In this work, an experimental verification is presented showing that pores can be imaged using short gradient pulses only. Experiments were carried out using hyperpolarized xenon gas in well-defined pores. The phase required for pore image reconstruction was retrieved from double diffusion encoded (DDE) measurements, while the magnitude could either be obtained from DDE signals or classical diffusion measurements with single encoding. The occurring image artifacts caused by restrictions of the gradient system, insufficient diffusion time, and by the phase reconstruction approach were investigated. Employing short gradient pulses only is advantageous compared to the initial long-narrow approach due to a more flexible sequence design when omitting the long gradient and due to faster convergence to the diffusion long-time limit, which may enable application to larger pores.

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.