We developed a simulation technique to study the effect of space charge interaction between trapped ions in the electrostatic ion beam trap (EIBT). The importance of space charge is demonstrated in both the dispersive and the self-bunching regime of the ion trap. The simulation results provide an estimate for the space charge effect on the trapping efficiency. They also allow for a better understanding of the enhanced diffusion and the self-bunching effect and provide a better characterization of the EIBT as a mass spectrometer, where peak coalescence is important. The numerical results reproduce all experimental data, demonstrating the critical importance of including space charge effects, even at low ion density, to understand the ion trap dynamics.

The $n$-vector spin model, which includes the self-avoiding walk (SAW) as a special case for the $n\to 0$ limit, has an upper critical dimensionality at four spatial dimensions (4D). We simulate the SAW on 4D hypercubic lattices with periodic boundary conditions by an irreversible Berretti-Sokal algorithm up to linear size $L=768$. From an unwrapped end-to-end distance, we obtain the critical fugacity as $z_c=0.147622380\left(2\right)$, improving over the existing result $z_c=0.1476223\left(1\right)$ by 50 times. Such a precisely estimated critical point enables us to perform a systematic study of the finite-size scaling of 4D SAW for various quantities. Our data indicate that near $z_c$, the scaling behavior of the free energy simultaneously contains a scaling term from the Gaussian fixed point and the other accounting for multiplicative logarithmic corrections. In particular, it is clearly observed that the critical magnetic susceptibility and the specific heat logarithmically diverge as $\chi \sim L^2{(lnL)}^{2{\widehat{y}}_h}$ and $C\sim {(lnL)}^{2{\widehat{y}}_t}$, and the logarithmic exponents are determined as ${\widehat{y}}_h=0.251\left(2\right)$ and ${\widehat{y}}_t=0.25\left(3\right)$, in excellent agreement with the field theoretical prediction ${\widehat{y}}_h={\widehat{y}}_t=1/4$. Our results provide a strong support for the recently conjectured finite-size scaling form for the $\mathrm{O}\left(n\right)$ universality classes at 4D.

In this paper we bring out the existence of a kind of synchronization associated with the size of a complex system. A dichotomic random jump process associated with the dynamics of an externally driven stochastic system with $N$ coupled units is constructed. We define an output frequency and phase diffusion coefficient. System size synchronization occurs when the average output frequency is locked to the external one and the average phase diffusion coefficient shows a very deep minimum for a range of system sizes. Analytical and numerical procedures are introduced to study the phenomenon, and the results describe successfully the existence of system size synchronization.

While the study of graphs has been very popular, simplicial complexes are relatively new in the network science community. Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial complexes provide a powerful mathematical framework to model such higher-order interactions. It is well known that the spectrum of the graph Laplacian is indicative of community structure, and this relation is exploited by spectral clustering algorithms. Here we propose that the spectrum of the Hodge Laplacian, a higher-order Laplacian defined on simplicial complexes, encodes simplicial communities. We formulate an algorithm to extract simplicial communities (of arbitrary dimension). We apply this algorithm to simplicial complex benchmarks and to real higher-order network data including social networks and networks extracted using language or text processing tools. However, datasets of simplicial complexes are scarce, and for the vast majority of datasets that may involve higher-order interactions, only the set of pairwise interactions are available. Hence, we use known properties of the data to infer the most likely higher-order interactions. In other words, we introduce an inference method to predict the most likely simplicial complex given the community structure of its network skeleton. This method identifies as most likely the higher-order interactions inducing simplicial communities that maximize the adjusted mutual information measured with respect to ground-truth community structure. Finally, we consider higher-order networks constructed through thresholding the edge weights of collaboration networks (encoding only pairwise interactions) and provide an example of persistent simplicial communities that are sustained over a wide range of the threshold.

Central pattern generators (CPGs) are relatively small neural networks that play a fundamental role in the control of animal locomotion. In this paper we define a method for the systematic design of CPG models able to exhibit biologically plausible gait transitions by implementing short-term synaptic plasticity mechanisms. As a case study, we focus on a simple CPG for quadruped locomotion. By applying the proposed method, three of four standard quadruped gaits were correctly reproduced by the obtained CPG model, not only in terms of the alternating sequence of the limbs but also in terms of frequency, duty cycle, and phase lags.

We report on the axisymmetric oscillation at the air-water interface in a food processor and Taylor-Couette systems. To gain insights into the mechanisms of free-surface oscillation, we conduct a series of experiments on the visual observations of free-surface deformation and the velocity measurements. At relatively low rotation speeds, the surface height at the rotating object surface decreases but remains stationary. As the rotation speed increases in small increments, oscillation begins when the deformed free surface detaches from the rotating object, and its onset depends strongly on the initial surface height. To account for the similarity mechanism of the onset, a scaled surface deformation based on the bulk Froude number is introduced herein; we find that the oscillation occurs at the scaled surface deformation beyond unity. These findings explain the causal relationship between the surface deformation and the oscillation onset and help to predict its occurrence to avoid mechanical damage to an apparatus with rotating components.

The effect of radiative heat transfer on the entropy generation in a two-phase nonisothermal fluid flow between two infinite horizontal parallel plates under the influence of a constant pressure gradient and transverse noninvasive magnetic field have been explored. Both fluids are considered to be viscous, incompressible, immiscible, Newtonian, and electrically conducting. The governing equations in Cartesian coordinates are solved analytically with appropriate boundary conditions to obtain the velocity and temperature profile inside the channel. Application of a transverse magnetic field is found to reduce the throughput and the temperature distribution of the fluids in a pressure-driven flow. The temperature and fluid flow inside the channel can also be noninvasively altered by tuning the magnetic field intensity, temperature difference between the channel walls and the fluids, and several intrinsic fluid properties. The entropy generation due to the heat transfer, magnetic field, and fluid flow irreversibilities can be controlled by altering the Hartmann number, radiation parameter, Brinkmann number, filling ratio, and ratios of fluid viscosities and thermal and electrical conductivities. The surfaces of the channel wall are found to act as a strong source of entropy generation and heat transfer irreversibility. The rate of heat transfer at the channel walls can also be tweaked by the magnetic field intensity, temperature differences, and fluid properties. The proposed strategies in the present study can be of significance in the design and development of next-generation microscale reactors, micro-heat exchangers, and energy-harvesting devices.

Oscillons, i.e., immobile spatially localized but temporally oscillating structures, are the subject of intense study since their discovery in Faraday wave experiments. However, oscillons can also disappear and reappear at a shifted spatial location, becoming jumping oscillons (JOs). We explain here the origin of this behavior in a three-variable reaction-diffusion system via numerical continuation and bifurcation theory, and show that JOs are created via a modulational instability of excitable traveling pulses (TPs). We also reveal the presence of bound states of JOs and TPs and patches of such states (including jumping periodic patterns) and determine their stability. This rich multiplicity of spatiotemporal states lends itself to information and storage handling.

This article presents micro-medium-amplitude oscillatory shear ($\mu \mathrm{MAOS}$), a method to measure the frequency-dependent micromechanical properties of soft materials in the asymptotically nonlinear regime using optical tweezers. We have developed a theoretical framework to extract these nonlinear mechanical properties of the material from experimental measurements and also proposed a physical interpretation of the third-order nonlinearities measured in single-tone oscillatory tests. We validate the method using a well-characterized surfactant solution of wormlike micelles, and subsequently employ this technique to demonstrate that the cytoplasm of a living cell undergoes strain softening and shear thinning when locally subjected to weakly nonlinear oscillatory deformations.

We investigate the flow of a viscous ferrofluid annulus surrounded by two nonmagnetic fluids in a Hele-Shaw cell when subjected to an external radial magnetic field. The interfacial pattern formation dynamics of the system is determined by the interplay of magnetic and surface tension forces acting on the inner and outer boundaries of the annulus, favoring the coupling of the disjoint interfaces. Mode-coupling analysis is employed to examine both linear and weakly nonlinear stages of the flow. Linear stability analysis indicates that the trailing and leading annular boundaries are coupled already at the linear regime, revealing that perturbations arising in the outer interface may induce the emergence of deformed structures in the inner boundary. Moreover, second-order weakly nonlinear analysis is utilized to identify key nonlinear morphological features of the ferrofluid annulus. Our theoretical results show that linear, $n$-fold symmetric annular patterns having rounded edges are replaced by nonlinear polygonal-like shapes, presenting fairly sharp fingers. It is found that, as opposed to the linear patterns, the nonlinear peaky structures reach a stationary state, characterized by a growth saturation process induced by nonlinear effects. Furthermore, the response of the ferrofluid ring to changes in the thickness of the annulus, in the relative strength of magnetic and surface tensions forces, as well as in the magnetic susceptibility of the ferrofluid material, are also discussed.

Particles moving in current sheets under extreme conditions, such as those in the vicinity of pulsars or those predicted on upcoming multipetawatt laser facilities, may be subject to significant radiation losses. We present an analysis of particle motion in model fields of a relativistic neutral electron-positron current sheet in the case when radiative effects must be accounted for. In the Landau-Lifshitz radiation reaction force model, when quantum effects are negligible, an analytical solution for particle trajectories is derived. Based on this solution, for the case when quantum effects are significant an averaged quantum solution in the semiclassical approach is obtained. The applicability region of the solutions is determined and analytical trajectories are found to be in good agreement with those of numerical simulations which account for radiative effects. Based on these results we demonstrate that radiation reaction itself can provide a mechanism of pinching even within a given field consideration.

Relaxation of the packing of elongated particles (discorectangles) aligned on a line was studied numerically. The aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;50]$. The initial jamming (saturated) state was produced using the basic variant of the random sequential adsorption model with random positions and orientations of particles. The relaxation was performed by allowing rotational and translational diffusion motions of the particles while their centers remained located on the line. The effects of the aspect ratio $\varepsilon$ on the kinetics of relaxation, the orientation order parameter, and the distribution function of the distances between nearest-neighbor discorectangles were analyzed. The transport properties of the resulting one-dimensional systems were also analyzed by using the diffusion of a tracer particle (random walker) between the nearest-neighbor discorectangles. In the relaxed states the anomalous diffusion was observed having a hopping exponent $d_w>2$ dependent upon $\varepsilon$.

We introduce an efficient dynamical tree method that enables us to explicitly demonstrate the thermoremanent magnetization memory effect in a hierarchical energy landscape. Our simulation nicely reproduces the nontrivial waiting-time and waiting-temperature dependences in this nonequilibrium phenomenon. We further investigate the condensation effect, in which a small set of microstates dominates the thermodynamic behavior in the multilayer trap model. Importantly, a structural phase transition of the multilayer tree model is shown to coincide with the onset of the condensation phenomenon. Our results underscore the importance of hierarchical structure and demonstrate the intimate relation between the glassy behavior and structure of barrier trees.

Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations and can give rise to constructive algorithms extracting relevant degrees of freedom. Efficient and reliable estimation or maximization of RSMI is, however, numerically challenging. A recent breakthrough in theoretical machine learning has been the introduction of variational lower bounds for mutual information, parametrized by neural networks. Here we describe in detail how these results can be combined with differentiable coarse-graining operations to develop a single unsupervised neural-network-based algorithm, the RSMI-NE, efficiently extracting the relevant degrees of freedom in the form of the operators of effective field theories, directly from real-space configurations. We study the information contained in the statistical ensemble of constructed coarse-graining transformations and its recovery from partial input data using a secondary machine learning analysis applied to this ensemble. In particular, we show how symmetries, also emergent, can be identified. We demonstrate the extraction of the phase diagram and the order parameters for equilibrium systems and consider also an example of a nonequilibrium problem.

The $\epsilon$-machine is a stochastic process's optimal model—maximally predictive and minimal in size. It often happens that to optimally predict even simply defined processes, probabilistic models—including the $\epsilon$-machine—must employ an uncountably infinite set of features. To constructively work with these infinite sets we map the $\epsilon$-machine to a place-dependent iterated function system (IFS)—a stochastic dynamical system. We then introduce the ambiguity rate that, in conjunction with a process's Shannon entropy rate, determines the rate at which this set of predictive features must grow to maintain maximal predictive power over increasing horizons. We demonstrate, as an ancillary technical result that stands on its own, that the ambiguity rate is the (until now missing) correction to the Lyapunov dimension of an IFS's attracting invariant set. For a broad class of complex processes, this then allows calculating their statistical complexity dimension—the information dimension of the minimal set of predictive features.

To better understand and optimize the capture of passive scalars (particles, pollutants, greenhouse gases, etc.) in complex geophysical flows, we study capture in the simpler, but still chaotic, time-dependent double-gyre flow model. For a range of model parameters, the domain of the double-gyre flow consists of a chaotic region, characterized by rapid mixing, interspersed with nonmixing islands in which particle trajectories are regular. Capture units placed within the domain remove all particles that cross their perimeters without altering the velocity field. To predict the capture capability of a unit at an arbitrary location, we characterize the trajectories of a uniformly seeded ensemble of particles as chaotic or nonchaotic, and then use them to determine the spatially resolved fraction of time that the flow is chaotic. With this information, we can predict where to best place units for maximum capture. We also examine the time dependence of the capture process, and demonstrate that there can be a trade-off between the amount of material captured and the capture rate.

The monomeric units of intrinsically disordered proteins self-assemble into oligomers, protofilaments, and eventually fibrils which may turn into amyloid. The aggregation of these proteins is primarily studied in bulk with no restriction on their degrees of freedom. Herein we experimentally demonstrate that amyloid-$\beta$ ($\mathrm{A}\beta$) aggregation under diffusion-limited conditions leads to its fractal self-assembly. Confocal microscopy and scanning electron microscopy with energy dispersion x-ray analysis were used to confirm that the fractal self-assemblies were formed from $\mathrm{A}\beta$ rather than the salt present in the two supporting media: deionized water and phosphate buffered saline. The results from the molecular docking experiments implicated that electrostatic and hydrophobic patches on the solvent-accessible surface area of the $\mathrm{A}\beta$ oligomers mediate the fractal self-assembly. These implications were tested with laser light scattering experiments on the oligomers formed by breaking mature fibrils of $\mathrm{A}\beta$ through sonication, which were observed to self-assemble into fractals when sonicated solutions were drop casted. The electrostatic interactions modulate the fractal morphologies with pH of the solution, which leads to a morphological phase transition observed through the variation in their fractal dimension. These transitions provide experimental evidence for the existing theoretical framework in terms of different kinetic models. The higher surface-to-volume ratio of these fractal self-assemblies may have applications in drug delivery, biosensing, and other biomedical applications.

When a drop impacts onto a pool of another liquid, the common interface will move down at a well-defined speed for the first few milliseconds. While simple mechanistic models and experiments with the same fluid used for the drop and pool have predicted this speed to be half the impacting drop speed, this is only one small part in a rich and intricate behavior landscape. Factors such as viscosity and density ratios greatly affect the penetration speed. By using a combination of high-speed photography, high-resolution numerical simulations, and physical modeling, we disentangle the different roles that physical fluid properties play in determining the true value of the postimpact interfacial velocity.

Mechanosensing of cells to extracellular matrix (ECM) is highly active and plays a crucial role in various physiological processes. Growing numbers of studies provide evidence that cell sensitivity to ECM stiffness is a complex stress-strain feedback process. However, the mechanisms that rule this process are still not fully known. Here, an alternative mechanosensing scheme of cells, which is different from the previous myosin-II-based mechanisms, is proposed by employing the tension in cortical cytoskeletons (CSKs) as a force module to probe the substrate. The molecular mechanotransduction from cortical CSKs, through actin filaments and focal adhesions, and finally to the substrate, is mechanically modeled to scale the dynamic traction forces of cells. The developed model captures the characteristic spread of cells with respect to ECM stiffness whereby the spread is fully developed on a stiff substrate but not on a soft one. Furthermore, durotactic migration of cells on an elastic-gradient substrate is successfully modeled by the current method. The cells are concluded to migrate, actuated by the polarized traction forces from the stiffness gradient of the substrate and the stiffness matching between cells and substrate. Finally, the cells are proposed to actively target the preferred substrate by following a rule of mechanical matching between cells and substrate. This study provides a theoretical tool to advance our knowledge regarding the passive mechanical properties and the active sensing of cells, and further promotes the discovery of mechanosensing mechanisms as well as the material design for embryonic development and tissue homeostasis.