Topological defects are singular points in vector fields, important in applications ranging from fingerprint detection to liquid crystals to biomedical imaging. In discretized vector fields, topological defects and their topological charge are identified by finite differences or finite-step paths around the tentative defect. As the topological charge is (half) integer, it cannot depend continuously on each input vector in a discrete domain. Instead, it switches discontinuously when vectors change beyond a certain amount, making the analysis of topological defects error prone in noisy data. We improve existing methods for the identification of topological defects by proposing a robustness measure for (i) the location of a defect, (ii) the existence of topological defects and the total topological charge within a given area, (iii) the annihilation of a defect pair, and (iv) the formation of a defect pair. Based on the proposed robustness measure, we show that topological defects in discrete domains can be identified with optimal trade-off between localization precision and robustness. The proposed robustness measure enables uncertainty quantification for topological defects in noisy discretized nematic fields (orientation fields) and polar fields (vector fields).

We experimentally investigate the dissolution of microscale sessile alcohol droplets in water under the influence of impermeable vertical confinement. The introduction of confinement suppresses the mass transport from the droplet to bulk medium in comparison with the nonconfined counterpart. Along with a buoyant plume, flow visualization reveals that the dissolution of a confined droplet is hindered by a mechanism called levitated toroidal vortex. The morphological changes in the flow due to the vortex-induced impediment alters the dissolution rate, resulting in enhancement of droplet lifetime. Further, we have proposed a modification in the key nondimensional parameters [Rayleigh number ${\mathrm{Ra}}^{\prime }$ (signifying buoyancy) and Sherwood number ${\mathrm{Sh}}^{\prime }$ (signifying mass flux)] and droplet lifetime ${{\tau }_c}^{\prime }$, based on the hypothesis of linearly stratified droplet surroundings (with revised concentration difference $\mathrm{\Delta }{C}^{\prime }$), taking into account the geometry of the confinements. We show that experimental results on droplet dissolution under vertical confinement corroborate scaling relations ${\mathrm{Sh}}^{\prime }\sim \mathrm{Ra}{{}^{\prime }}^{1/4}$ and ${{\tau }_c}^{\prime }\sim \mathrm{\Delta }C{{}^{\prime }}^{-5/4}$. We also draw attention to the fact that the revised scaling law incorporating the geometry of confinements proposed in the present work can be extended to other known configurations such as droplet dissolution inside a range of channel dimensions, as encountered in a gamut of applications such as microfluidic technology and biomedical engineering.

The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of ${\mathrm{SF}}_6\text{−}\mathrm{He},{\mathrm{SF}}_6\text{−}{\mathrm{D}}_2$, and ${\mathrm{SF}}_6\text{−}{\mathrm{H}}_2$. In these measurements, the pressure of the gases with heavy molecular mass $\left({\mathrm{SF}}_6\right)$ is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of ${\mathrm{SF}}_6$ and the very small polarizabilities of He, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy ${\mathrm{SF}}_6$ molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy ${\mathrm{SF}}_6$ molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter $z$ that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter $z$ is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.

Pinned solitons are a special class of nonlinear solutions created by a supersonically moving object in a fluid. They move with the same velocity as the moving object and thereby remain pinned to the object. A well-known hydrodynamical phenomenon, they have been shown to exist in numerical simulation studies but to date have not been observed experimentally in a plasma. In this paper we report the first experimental excitation of pinned solitons in a dusty (complex) plasma flowing over a charged obstacle. The experiments are performed in a $\mathrm{\Pi }$ shaped dusty plasma experimental (DPEx) device in which a dusty plasma is created in the background of a DC glow discharge Ar plasma using micron sized kaolin dust particles. A biased copper wire creates a potential structure that acts as a stationary charged object over which the dust fluid is made to flow at a highly supersonic speed. Under appropriate conditions nonlinear stationary structures are observed in the laboratory frame that correspond to pinned structures moving with the speed of the obstacle in the frame of the moving fluid. A systematic study is made of the propagation characteristics of these solitons by carefully tuning the flow velocity of the dust fluid by changing the height of the potential structure. It is found that the nature of the pinned solitons changes from a single-humped one to a multihumped one and their amplitudes increase with an increase of the flow velocity of the dust fluid. The experimental findings are then qualitatively compared with the numerical solutions of a model forced Korteweg de Vries (fKdV) equation.

A random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food. In this paper we take a target-centric viewpoint by considering the accumulation of resources in one or more targets due to multiple rounds of search-and-capture events combined with resource degradation; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position. The searcher is then resupplied with cargo and a new search process is initiated after a random delay. It has previously been shown how queuing theory can be used to derive general expressions for the steady-state mean and variance of the resulting resource distributions. Here we apply the theory to some classical FPT problems involving diffusion in simple geometries with absorbing boundaries, including concentric spheres, wedge domains, and branching networks. In each case, we determine how the resulting Fano factor depends on the degradation rate, the delay distribution, and various geometric parameters. We thus establish that the Fano factor can deviate significantly from Poisson statistics and exhibits a nontrivial dependence on model parameters, including nonmonotonicity and crossover behavior. This indicates the nontrivial nature of the higher-order statistics of resource accumulation.

The Fortuin-Kasteleyn (FK) random-cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the critical Ising model ($q=2$) on a finite complete graph, i.e., the mean-field Ising model. We provide strong numerical evidence that the configuration space for $q=2$ contains an asymptotically vanishing sector in which quantities exhibit the same finite-size scaling as in the critical uncorrelated bond percolation ($q=1$) on the complete graph. Moreover, we observe that, in the full configuration space, the power-law behavior of the cluster-size distribution for the FK Ising clusters except the largest one is governed by a Fisher exponent taking the value for $q=1$ instead of $q=2$. This demonstrates the percolation effects in the FK Ising model on the complete graph.

Dynamic-mode decomposition (DMD) is a well-established data-driven method of finding temporally evolving linear-mode decompositions of a nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled through measurement. To address dynamical systems in which the data may be incomplete or represent only partial observation of a more complex system, we extend the DMD algorithm by including a Mori-Zwanzig decomposition to derive memory kernels that capture the averaged dynamics of the unresolved variables as projected onto the resolved dimensions. From this, we then derive what we call the memory-dependent dynamic mode decomposition (MDDMD). Through numerical examples, the MDDMD method is shown to produce reasonable approximations of the ensemble-averaged dynamics of the full system given a single time series measurement of the resolved variables.

We investigated the bifurcation structure on the self-propelled motion of a camphor rotor at a water surface. The center of the camphor rotor was fixed by the axis, and it showed rotational motion around it. Due to the chiral asymmetry of its shape, the absolute values of the angular velocities in clockwise and counterclockwise directions were different. This asymmetry in the angular velocities implies an imperfect bifurcation. From the numerical simulation results, we discuss the condition for the occurrence of the imperfect bifurcation.

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the $1/4^{\circ }$ ($\sim 25$ km) model, advection has a substantial impact on the rate of primary productivity, while the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sublinearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore, we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the nonlinear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low-complexity (e.g., RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

We theoretically and computationally find a Maxwell-Boltzmann-like velocity distribution for noninteracting active matter (NAM). To achieve this, mass and moment of inertia are incorporated into the corresponding noninteracting active Fokker-Planck equation (NAFP), thus solving for the first time, the underdamped scenario of NAM following a Fokker-Planck formalism. This time, the distribution results in a bimodal symmetric expression that contains the effect of inertia on transport properties of NAM. The analytical distribution is further compared to experiments dealing with vibrobots. A generalization of the Brinkman hierarchy for NAFP is also provided and used for systematically solving the NAFP in position space. This work is an important step toward characterizing active matter using an equivalent nonequilibrium statistical mechanics.

We present a simple model system with four hard disks moving in a circular region for which free-energy landscapes can be directly calculated and visualized in two and three dimensions. We construct several energy landscapes for our system, and we explore the strengths and limitations of each in terms of understanding system dynamics, in particular the relationship between state transitions and free-energy barriers. We also demonstrate the importance of distinguishing between system dynamics in real space and those in landscape coordinates, and we show that care must be taken to appropriately combine dynamics with barrier properties to understand the transition rates. This simple model provides an intuitive way to understand free-energy landscapes, and it illustrates the benefits that free-energy landscapes can have over potential energy landscapes.

We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM) near the dimension $d_{\mathrm{DR}}\approx 5.1$ that separates a region where the renormalized theory at the fixed point is supersymmetric and critical scaling satisfies the $d\to d-2$ dimensional reduction property ($d>d_{\mathrm{DR}}$) from a region where both supersymmetry and dimensional reduction break down at criticality ($d<d_{\mathrm{DR}}$). We show that the NP-FRG results are in very good agreement with recent large-scale lattice simulations of the RFIM in $d=5$ and we detail the consequences for the leading correction-to-scaling exponent of the peculiar boundary-layer mechanism by which the dimensional-reduction fixed point disappears and the dimensional-reduction-broken fixed point emerges in $d_{\mathrm{DR}}$.

Adding transitions to an equilibrium system increases the activity. Naively, one would expect this to hold also in out-of-equilibrium systems. We demonstrate, using relatively simple models, how adding transitions to an out of equilibrium system may in fact reduce the activity and even cause it to vanish. This surprising effect is caused by adding heretofore forbidden transitions into less and less active states. We investigate six related kinetically constrained lattice gas models, some of which behave as naively expected while others exhibit this nonintuitive behavior. These models exhibit an absorbing state phase transition, which is also affected by the added transitions. We introduce a semi-mean-field approximation describing the models, which agrees qualitatively with our numerical simulation.

Ion attachment and ion drag to dust particles near the edge of a nonthermal plasma sheath are of interest to better understand how particles become trapped in such sheath regions. While electron-particle collisions in plasmas and sheaths can often be described by orbital motion limited theory, quantification of ion transport about dust particles in collisional sheath regions requires a distinct modeling approach. In this work, the dimensionless ion attachment coefficients and dimensionless collection forces on negatively charged particles are calculated using ion trajectory models accounting for an external electric field in a collisional sheath, ion inertia, and finite ion mobility. By considering both ion inertia and finite ion mobility, results apply for ion transport from the fully collisional regime into a regime of intermediate collisionality. Ion collection forces are calculated in two related limits; first, the nondissipative limit, wherein the dimensionless collection force function coincides with the dimensionless attachment coefficient (anticipated in the collisionless regime), and second, a dissipative limit, wherein neutral gas collisions dissipate ion momentum, which strongly affects the resulting collection force (anticipated in the fully collisional regime). We show that ion motion about a charged particle can be parametrized by the ion Stokes number, which is the ratio of ion inertia to gas resistance to motion and dimensionless electric field strength (the external field strength normalized by the electric field at the particle surface). At intermediate Stokes numbers (${10}^1–{10}^2$), ions adopt trajectories that are extremely sensitive to the initial ion-particle impact parameter. Plots of the resulting collision angle at fixed Stokes number and dimensionless field strength as a function of impact parameter contain multiple discontinuities. Nonetheless, we obtain smooth curves for the ion attachment rates and collection forces in both the nondissipative and fully dissipative limits. Increasing the ion Stokes number is found to significantly decrease the dimensionless ion attachment coefficients and ion collection forces in comparison to coefficients evaluated with expressions derived in the fully collisional limit. In all instances, including the dissipative limit, we find the ion collection force acts in the direction of ion migration. Neural network fits are utilized to parametrize the resulting attachment coefficients and ion collection forces, and we apply these fits to examine the charge levels on 1-μm radius particles in external fields in the $3\times {10}^2–3\times {10}^3\mathrm{V}{\mathrm{m}}^{-1}$ range and pressures in the $5\times {10}^{-1}–5\times {10}^1$ Torr (66.7–6667 Pa) range. We find the charge level is strongly sensitive to both field strength and pressure in the plasma sheath, ranging from 2 × ${10}^2$ to 2 × ${10}^3$ over the conditions examined. Calculations are also used to demonstrate that the ion collection force can be sufficiently strong to trap particles not only close to the bottom electrode of a parallel-plate reactor, but also close to the top electrode, with a critical ion density required for trapping.

We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an $N$-component complex scalar field with integer charge $q$, so that they have local U(1) and global $\mathrm{SU}(N$) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge $q$ of the scalar field and the number $N\ge 2$ of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global $\mathrm{SU}(N$) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number $N$ of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global $\mathrm{SU}(N$) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., $N=2$ and $N=25$.

One of the fundamental questions in the emerging field of quantum thermodynamics is the role played by coherence in energetic processes that occur at the quantum level. Here we address this issue by investigating two different quantum versions of the first law of thermodynamics, derived from the classical definitions of work and heat. By doing so, we find out that there exists a mathematical inconsistency between both scenarios. We further show that the energetic contribution of the dynamics of coherence is the key ingredient to establish the consistency. Some examples involving two-level atomic systems are discussed in order to illustrate our findings.

The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is demonstrated that the super-Gaussian function gives a good approximation for profiles of fundamental QDs and droplets with nonzero vorticity. The dynamical equations for parameters of QDs are obtained. Fixed points of these equations determine the parameters of stationary QDs. The period of small oscillations of QDs near the stationary state is estimated. It is obtained that periodic modulations of the strength of quantum fluctuations can actuate different processes, including resonance oscillations of the QD parameters, an emission of waves and a splitting of QDs into smaller droplets.

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.

Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulation captures the effect of the type of imposed pressure oscillations on the migration pattern of the capsule. An oscillatory channel flow enables the focusing of extremely small biological particles by eliminating the need to design impractically long channels. The presented results show that the equilibrium position of the capsule changes not only by the addition of an oscillatory component to the pressure gradient but it also is influenced by the capsule deformability and channel flow rate. Furthermore, it has been shown that the amplitude of oscillation of capsules decreases as the channel flow rate and the rigidity of the capsule increases.

A new set of thermodynamically consistent Onsager-Burnett equations [Singh, Jadhav, and Agrawal, Phys. Rev. E 96, 013106 (2017)] has recently been derived. In this work, we subject these equations to a severe test case of strong shock (Mach number = 134) for a dilute gas system composed of hard-sphere molecules. The numerical results of OBurnett equations for conserved and nonconserved variables are compared against the molecular dynamics and direct simulation Monte Carlo results available in the literature. With no tweaking of the equations in any way, we establish several fundamental aspects of OBurnett equations which other higher-order continuum theories like Burnett and Grad equations lack. In particular, evidence is put forward for smooth shock structures, the existence of heteroclinic trajectory, and positive entropy generation inside the shock at all Mach numbers. With respect to shock profiles of hydrodynamic variables, it is observed that OBurnett equations significantly improve upon the results of Navier-Stokes equations. Further comparison with regularized 13 (R13) equations at lower Mach numbers shows that OBurnett equations capture the more rarefied upstream part better than the R13 equations. These evidences suggest that the OBurnett equations are accurate and form a reliable set of higher-order transport equations. Further, it should now be possible to describe the complex structure of the shock wave correctly, even at a very large Mach number.