Finite Velocity Research Articles

Sharp interface limit of a two-time scale phase field model of a binary mixture.

Due to its analytical flexibility and thermodynamic consistency, the phase field model is widely used in the analysis of equilibrium states and transformation between phases. The present review is devoted to one of the classes of kinetic models in the form of the hyperbolic phase field, which is applicable to slow and fast phase transformations. In the example of solidification from metastable liquid, the analysis is presented for the important procedure of reducing of the diffuse interface to the sharp interface. A special asymptotic analysis is discussed for application to solidifying binary mixture with diffuse phase interface under arbitrary concentration of species and under isothermal and isobaric conditions. Asymptotic analysis states that the hyperbolic phase field model arrives at the known hyperbolic Stefan problem within the sharp interface limit. The solution of this problem together with the common tangent construction allows us to analyze ($i$) nonequilibrium effect in the form of solute trapping and ($ii$) the complete transition from the diffusion-limited to the diffusionless (chemically partitionless) solidification at the finite interface velocity. A comparison with other theoretical models is summarized and the discussion on accessible experimental results is given.

Hyperbolic Diffusion Functionals on a Ring with Finite Velocity

I study a lattice with periodic boundary conditions using a non-local master equation that evolves over time. I investigate different system regimes using classical theories like Fisher information, Shannon entropy, complexity, and the Cramér–Rao bound. To simulate spatial continuity, I employ a large number of sites in the ring and compare the results with continuous spatial systems like the Telegrapher’s equations. The Fisher information revealed a power-law decay of t−ν, with ν=2 for short times and ν=1 for long times, across all jump models. Similar power-law trends were also observed for complexity and the Fisher information related to Shannon entropy over time. Furthermore, I analyze toy models with only two ring sites to understand the behavior of the Fisher information and Shannon entropy. As expected, a ring with a small number of sites quickly converges to a uniform distribution for long times. I also examine the Shannon entropy for short and long times.

Self-assembly of active bifunctional Brownian particles.

In this work, with the intent of exploring the out-of-equilibrium polymerization of active patchy particles in linear chains, we study a suspension of active bifunctional Brownian particles (ABBPs). At all studied temperatures and densities, ABBPs self-assemble in aggregating chains, as opposed to the uniformly space-distributed chains observed in the corresponding passive systems. The main effect of activity, other than inducing chain aggregation, is to reduce the chain length and favour the alignment of the propulsion vectors in the bonding process. At low activities, attraction dominates over activity in the bonding process, causing self-assembly to occur randomly regardless of the particle orientations. Interestingly, we find that at the lowest temperature, as density increases, chains aggregate forming a novel state: MISP, i.e., motility-induced spirals, where spirals are characterised by a finite angular velocity. In contrast, at the highest temperature, density and activity, chains aggregate forming a different novel state (a spinning crystalline cluster) characterised by a compact and hexagonally ordered structure, both translating and rotating. The rotation arises from an effective torque generated by the presence of competing domains where particles self-propel in the same direction.

Rydberg atomic spectroscopy based on nanosecond pulsed laser excitation

<sec>Through the cascade excitation of 852-nm continuous-wave (CW) laser and 509-nm nanosecond pulsed laser, the electromagnetically-induced transparency (EIT) spectroscopic signals of ladder-type three-level cesium atoms with Rydberg state are obtained by using a room-temperature cesium vapor cell. The power of 509-nm pulsed laser beam is ~176 W, while the pulse repetition frequency ranges from 300 kHz to 100 MHz and can be continuously adjusted. The laser pulse duration runs from 1 to 100 ns and can be continuously adjusted. The relationship between Rydberg EIT spectroscopic signals and 509-nm nanosecond pulsed laser parameters is investigated experimentally. By changing the pulse repetition frequency and the pulse duration of the 509-nm nanosecond pulsed laser, the comb-like Rydberg atomic spectrum is obtained by using a room-temperature cesium vapor cell. Within a certain range of repetition frequency and pulse duration, the envelope of spectral lines shows a regular pattern, and the spacing between the transmission peaks is consistent with the pulse repetition frequency. By changing the 509-nm laser pulse repetition frequency and pulse duration, atoms with the specific velocity group can be excited to Rydberg state. </sec><sec>Reducing the repetition frequency of the 509-nm pulsed coupling laser can further increase the number of atoms in the Rydberg state in comparison with the case of finite velocity group pumping of cesium atoms by a continuous-wave laser. When the repetition frequency of the 509-nm pulsed laser approaches the EIT linewidth, the number of cesium Rydberg atoms can be increased by up to 10 times. In the parameter optimization process, the dynamic characteristics of pulsed excitation in multi-level atoms, as well as the interaction characteristics between arbitrarily shaped laser pulses and multi-level atomic systems, should be considered. Pulsed laser pumping can achieve the interaction between the laser field and atomic group with a specific velocity, and its developed atomic frequency comb spectra can be used for electric and magnetic field measurements. The multi-peak structure of the spectrum can be used to more accurately determine the intensity, frequency, and phase of the microwave electric field by measuring spectral variations. This high-sensitivity and high-resolution measurement capability is crucial for precisely measuring microwave electric fields. The pulsed coupling laser can excite atoms in a specific velocity group to the Rydberg state. High-density Rydberg atoms can improve the signal-to-noise ratio of the measured spectrum, which has potential applications in quantum sensing and quantum measurement based on Rydberg atoms.</sec>

The Spatiotemporal Structure of Induced Magnetic Fields in Callisto's Plasma Environment Due to Their Propagation With MHD Modes

AbstractWe investigate how the spatiotemporal structure of induced magnetic fields outside of Callisto is affected by their propagation with the magnetohydrodynamic (MHD) modes. At moons that are surrounded by dense magnetized plasmas like the Galilean moons, low‐frequency induced magnetic fields cannot propagate with the ordinary electromagnetic mode as is implicitly used by standard analytical expressions. Instead, the induced magnetic fields propagate with the MHD modes, which exhibit anisotropic propagation properties and have finite velocities. Using an MHD framework, we model the spatiotemporal effects of the transport on the induced signals and analyze their contribution to Galileo's C03 and C09 flyby observations. We find that the induced magnetic field in Callisto's plasma environment is asymmetric with a pronounced upstream/downstream asymmetry. By neglecting the transport effects, the amplitude of the induced magnetic field is under‐ or overestimated by up to tens of percent, respectively. Additionally, we find that MHD wave and convection velocities are strongly reduced in Callisto's local plasma environment, resulting in an additional temporal delay between the emergence of the induced field at the surface of Callisto or the top of its ionosphere and the measurements at spacecraft location. The associated phase shift depends on the location of the observer and can reach values of several to tens of degrees of the phase of the primary inducing frequency. Transport effects impact the observed induction signals and are consistent with the C03 and C09 magnetic field measurements.

Holographic zero sound for [formula omitted] SCFTs in 4d

We build up the notion of metallic holography for N=2 SCFTs in four dimensions, in the presence of a finite U(1) chemical potential. We compute two point correlation functions and study their properties in the regime of low frequency and low momentum. The color sector reveals gapless excitations, one of which propagates with a finite phase velocity while the other mode attenuates through scattering. The flavour sector, on the other hand, reveals spectrum that contains quasiparticle excitations which propagate with a definite phase velocity together with modes that propagate with a finite group velocity which quantum attenuates quite similar in spirit as that of Landau's zero sound modes. We also compute associated AC conductivities, which exhibit different characteristics for different (color and flavour) sectors of N=2 SCFTs.

Slip due to kink propagation at the liquid–solid interface

In Couette flow, the liquid atoms adjacent to a solid substrate may have a finite average tangential velocity relative to the substrate. This so-called slip has been observed frequently. However, the particular molecular-level mechanisms that give rise to liquid slip are poorly understood. It is often assumed that liquid slip occurs by surface diffusion whereby atoms independently move from one substrate equilibrium site to another. We show that under certain conditions, liquid slip is due not to singular independent molecular motion, but to localized nonlinear waves that propagate at speeds that are orders of magnitude greater than the slip velocity at the liquid–solid interface. Using non-equilibrium molecular dynamics simulations, we find the properties of these waves and the conditions under which they are to be expected as the main progenitors of slip. We also provide a theoretical guide to the properties of these nonlinear waves by using an augmented Frenkel–Kontorova model. The new understanding provided by our results may lead to enhanced capabilities of the liquid–solid interface, for heat transfer, mixing, and surface-mediated catalysis.

Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations

Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.

Interplay Between Nucleation and Kinetics in Dynamic Twinning

Abstract In this work, we apply a phase-field modeling framework to elucidate the interplay between nucleation and kinetics in the dynamic evolution of twinning interfaces. The key feature of this phase-field approach is the ability to transparently and explicitly specify nucleation and kinetic behavior in the model, in contrast to other regularized interface models. We use this to study two distinct problems where it is essential to explicitly specify the kinetic and nucleation behavior governing twin evolution. First, we study twinning interfaces in 2D. When these interfaces are driven to move, we find that significant levels of twin nucleation occur ahead of the moving interface. Essentially, the finite interface velocity and the relaxation time of the stresses ahead of the interface allow for nucleation to occur before the interface is able to propagate to that point. Second, we study the growth of needle twins in antiplane elasticity. We show that both nucleation and anisotropic kinetics are essential to obtain predictions of needle twins. While standard regularized interface approaches do not permit the transparent specification of anisotropic kinetics, this is readily possible with the phase-field approach that we have used here.

Inertial migration of rigid particles in shear-thinning fluids under asymmetric wall slip conditions

The determination of flow-induced equilibrium positions in pressure-driven flows in microchannels is of great practical importance in particle manipulation. In the computational analysis presented in this paper, the inertial ordering of neutrally buoyant rigid spheres in shear-thinning fluid flow through a hydrophobic microchannel is investigated. The combined effect of the viscosity index n of a power-law fluid and fluid slippage at the wall on the lateral focusing of microspheres is examined in detail. Using the finite element method, the Eulerian flow field between partially slipping parallel walls is simulated, and the Lagrangian movement of particles is continuously tracked. The Navier slip model is used to ensure a finite fluid velocity at the wall, and it is tuned by modifying the slip-length. It is observed that inertial particles concentrate at a standard equilibrium position of 0.6 times the channel half-width H, irrespective of fluid slip due to the symmetry of the flow field. However, this equilibrium position shifts closer to the walls as the viscosity index increases; for instance, when n = 0.5, particles stabilize at 0.75H. As a consequence of asymmetry in hydrodynamic behavior due to different fluid slippages at the upper and lower walls, the particle migration path is altered. In a channel with a no-slip upper wall and a partially slipping lower wall (β/H = 0.4), particles settle closer to the lower wall at 0.8H. Most importantly, the lateral movement of a particle released at a given vertical position can be altered by tailoring the wall hydrophobicity and viscosity index, thus enabling multiple equilibrium locations to be achieved.

Chiral phase transition and spin alignment of vector mesons in the polarized-Polyakov-loop Nambu–Jona-Lasinio model under rotation

By using the analytic continuation method, a polarized Polykov-loop potential at finite real angular velocity is constructed from the lattice results at finite imaginary angular velocity. The chiral and deconfinement phase transitions under rotation have been simultaneously investigated in the polarized-Polyakov-loop Nambu–Jona-Lasinio (PPNJL) model. It is observed that both critical temperatures of deconfinement and chiral phase transition increase with the angular velocity, which is in consistent with lattice results. The spin alignment of vector meson has the negative deviation of ρ00−1/3 under rotation, and the deviation in the PPNJL model is much more significant than that in the NJL model and the quark coalescence model, which revealing the important role of rotating gluons on the quark polarization. Published by the American Physical Society 2024

Lieb-Robinson correlation function for the quantum transverse-field Ising model

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function. Published by the American Physical Society 2024

Spin-orbit torque-driven domain wall motion in the absence of Dzyaloshinskii-Moriya interactions

The fine structure and dynamics of magnetic domain walls in ultrathin films with perpendicular magnetization, in the presence of a secondary anisotropy, is analysed owing to micromagnetics. Two cases are considered, a cubic anisotropy typical for (111) oriented garnet epitaxial films, and an orthorhombic anisotropy as found in, e.g., Co/W(110) films. The statics is solved first, showing that, in general, domain walls are not of the pure Bloch type. The dynamics under the spin Hall effect induced by a current flowing in an adjacent layer is then monitored. Finite and non-negligible domain wall velocities are predicted in both cases, in the absence of Dzyaloshinskii-Moriya interactions, with distinct behaviours regarding the current density and its orientation with respect to the secondary anisotropy axes. The relevance of these results to recent reports of current-driven domain wall dynamics in insulating ultrathin garnet films, capped with platinum, is discussed.

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis.

Discrete heat equations for the multilayered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in ω-k space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, and phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers. These functions demonstrate unusual behavior at high frequency compared to the continuum case. Furthermore, the maximum allowed frequency and wave number for the discrete heat equation are limited, whereas there are no such limits in a continuum. The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and timescales the discrete approach is preferable. This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing one to study ultrafast wavelike heat conduction regimes in periodic multilayered metamaterials.

Multidimensional random motions with a natural number of finite velocities

AbstractWe present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some broad assumptions, we give the joint distribution of the position of the motion (for both the inner part and the boundary of the support) and the number of displacements performed with each velocity. Explicit results for cyclic and complete motions are derived. We establish useful relationships between motions moving in different spaces, and we derive the form of the distribution of the movements in arbitrary dimension. Finally, we investigate further properties for stochastic motions governed by non-homogeneous Poisson processes.

Coalescence of non-spherical drops with a liquid surface

We employ three-dimensional numerical simulations to explore the impact dynamics of non-spherical drops in a deep liquid pool by varying the aspect ratios (Ar) and Weber numbers (We). We observe that when a non-spherical drop is gently placed on a liquid pool, it exhibits a partial coalescence phenomenon and the emergence of a daughter droplet for Ar>0.67. In contrast to the prolate (Ar<1) and spherical drops (Ar=1), an oblate (Ar>1) drop with a high aspect ratio encapsulates air in a ring-like bubble within the pool and emerges a liquid column that undergoes Rayleigh–Plateau capillary instability, leading to the formation of two daughter droplets with complex shapes. When the parent drop is impacted with finite velocity, our observations indicate that increasing the Weber number leads to elevated crater heights on the free surface for all aspect ratios. A prolate drop produces a less pronounced wave swell and exhibits a prolonged impact duration owing to its negligible impact area. Conversely, an oblate drop generates a much wider wave swell than spherical and prolate drops. We analyze the relationship between rim formation dynamics and the kinetic and surface energies of the system. Finally, we establish an analogy by comparing the dynamics of a freely falling non-spherical drop, undergoing topological oscillations during its descent from a height, with the impact dynamics of parent drops of various shapes striking the liquid surface with an equivalent velocity. Our investigation involving non-spherical drops contrasts the extensive studies conducted by various researchers on the impact of a parent spherical drop just above the free surface of a liquid pool.

3D cylindrical BGK model of electron phase-space holes with finite velocity and polarization drift

Nonlinear kinetic structures, called electron phase-space holes (EHs), are regularly observed in space and experimental magnetized plasmas. The existence of EHs is conditioned and varies according to the ambient magnetic field and the parameters of the electron beam(s) that may generate them. The objective of this paper is to extend the 3D Bernstein–Greene–Kruskal model with cylindrical geometry developed by L.-J. Chen et al. [“Bernstein–Greene–Kruskal solitary waves in three-dimensional magnetized plasma,” Phys. Rev. E 69, 055401 (2004)] and L.-J. Chen et al., [“On the width-amplitude inequality of electron phase space holes,” J. Geophys. Res. 110, A09211 (2005)] to include simultaneously finite effects due to (i) the strength of the ambient magnetic field B0, by modifying the Poisson equation with a term derived from the electron polarization current, and (ii) the drift velocity ue of the background plasma electrons with respect to the EH, by considering velocity-shifted Maxwellian distributions for the boundary conditions. This allows us to more realistically determine the distributions of trapped and passing particles forming the EHs, as well as the width-amplitude relationships for their existence.

Distributed control of partial differential equations using convolutional reinforcement learning

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational equivariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents’ environment can be drastically reduced using a convolution operation over the state space of the PDE, by which we effectively tackle the curse of dimensionality otherwise present in deep reinforcement learning. In this setting, the complexity can be flexibly adjusted via the kernel width or by using a stride greater than one (meaning that we do not place an actuator at each sensor location). Moreover, scaling from smaller to larger domains – or the transfer between different domains – becomes a straightforward task requiring little effort. We demonstrate the performance of the proposed framework using several PDE examples with increasing complexity, where stabilization is achieved by training a low-dimensional deep deterministic policy gradient agent using minimal computing resources.

Coupled models for propagation of explosive shock waves in cylindrical and spherical geometries

The propagation of shock waves in different geometries is crucial in engineering and scientific applications. A comprehensive model is developed to elucidate the hydrodynamic growth and decay of shock waves in cylindrical and spherical geometries by using the strong shock wave assumption. This model takes into consideration the conservation equations governing mass, momentum, and energy, thereby allowing for an accurate description of the coupled behavior between the piston and shock wave propagation. In contrast to the localized analysis employed in previous self-similar methods, this model incorporates the finite sound wave velocity to introduce the concept of retarded pressure on the piston surface. Consequently, the proposed model offers a multitude of advantages by providing a complete set of dynamic information concerning the trajectories, velocities, and accelerations of both the piston and shock wave. Furthermore, an asymptotic analytical solution is derived to describe the decay of shock waves in cylindrical and spherical geometries. To validate the theoretical analysis and illustrate the propagation characteristics of shock waves in these specific geometries, thorough comparisons are conducted. These findings contribute to the advancement of our understanding of shock wave dynamics in various physical systems, particularly in the field of plasma physics.

A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces

A conservative implicit scheme in the finite volume discrete velocity method framework is proposed for solving the three-dimensional steady flows of molecular gases in all flow regimes from continuum one to free-molecular one. This work is based on the Boltzmann–Rykov model equation, which is a nonlinear relaxation model and can describe the thermodynamic non-equilibrium of diatomic gas flows. The macroscopic equations are solved implicitly together with the Rykov model equation to find a predicted equilibrium distribution first at each iteration step. As a result, the collision term of the Rykov model equation can be discretized in a fully implicit way for fast convergence in all flow regimes. At the cell interface, an asymptotic preserving simplified multi-scale numerical flux is developed to relieve the limitation of grid size and time step in all flow regimes, which can keep the multi-scale property and achieve high computational efficiency. The integral error compensation technique is used to keep the scheme conservative and greatly reduce the number of unstructured discrete velocity space (DVS) meshes. Furthermore, an empirical criterion based on the numerical experiments of the Apollo 6 command module is suggested to guide the generation of three-dimensional unstructured DVS. The accuracy and efficiency of the present method are demonstrated by a number of three-dimensional classic cases, covering different flow regimes.