arXiv subjects

Satoshi Takada

Publications and source records attributed to Satoshi Takada.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multiple quantum Mpemba effect: exceptional points and oscillations

We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to $multiple$ quantum Mpemba effect. It occurs in an observable when time evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies i.e. the copy with higher observable value before the intersection becomes the lower valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature etc. exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.

quant-ph↗

arXiv2023

Revisiting stress propagation in a two-dimensional elastic circular disk under diametric loading

In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines.

cond-mat.soft↗

arXiv2023

Rheology of a dilute binary mixture of inertial suspension under simple shear flow

The rheology of a dilute binary mixture of inertial suspension under simple shear flow is analyzed in the context of the Boltzmann kinetic equation. The effect of the surrounding viscous gas on the solid particles is accounted for by means of a deterministic viscous drag force plus a stochastic Langevin-like term defined in terms of the environmental temperature $T_\text{env}$. Grad's moment method is employed to determine the temperature ratio and the pressure tensor in terms of the coefficients of restitution, concentration, the masses and diameters of the components of the mixture, and the environmental temperature. Analytical results are compared against event-driven Langevin simulations for mixtures of hard spheres with the same mass density $m_1/m_2=(σ^{(1)}/σ^{(2)})^3$, $m_i$ and $σ^{(1)}$ being the mass and diameter, respectively, of the species $i$. It is confirmed that the theoretical predictions agree with simulations of various size ratios $σ^{(1)}/σ^{(2)}$ and for elastic and inelastic collisions in the wide range of parameters' space. It is remarkable that the temperature ratio $T_1/T_2$ and the viscosity ratio $η_1/η_2$ ($η_i$ being the partial contribution of the species $i$ to the total shear viscosity $η=η_1+η_2$) discontinuously change at a certain shear rate as the size ratio increases; this feature (which is expected to occur in the thermodynamic limit) cannot be completely captured by simulations due to small system size. In addition, a Bhatnagar--Gross--Krook (BGK)-type kinetic model adapted to mixtures of inelastic hard spheres is exactly solved when $T_\text{env}$ is much smaller than the kinetic temperature $T$. A comparison between the velocity distribution functions obtained from Grad's method, BGK model, and simulations is carried out.

cond-mat.soft↗

arXiv2023

Quantum Mpemba effect in a quantum dot with reservoirs

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold), cross each other at finite time (and thereby reverse their identities i.e. hot becomes cold and vice versa) to generate thermal quantam Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems, does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

cond-mat.stat-mech↗

arXiv2022

Rheology of dilute granular gas mixtures where the grains interact via a square shoulder and well potential

We develop the rheology of a dilute granular gas mixture. Motivated by the interaction of charged granular particles, we assume that the grains interact via a square shoulder and well potential. Employing kinetic theory, we compute the temperature and the shear viscosity as functions of the shear rate. Numerical simulations confirm our results above the critical shear rate. At a shear rate below a critical value, clustering of the particles occurs.

cond-mat.stat-mech↗

arXiv2022

Drag of an elliptic intruder in a two-dimensional granular environment

The drag of an elliptic intruder in a two-dimensional granular environment is numerically studied. The movement parallel to the major axis of the intruder is found to be unstable. The drag law is given by the sum of the yield force and the dynamic term, the latter of which is approximately reproduced by a simple collision model. The flow field around the intruder for sufficiently larger drag force is well fitted by the streamlines obtained from the perfect fluid. The stress fields around the intruder are also investigated when the movement of the intruder is balanced with interactions with the surrounding particles. The Airy stress function is found to well reproduce the stress fields once the stress on the surface of the intruder is given.

cond-mat.soft↗

arXiv2022

Drag of Two Cylindrical Intruders in a Two-Dimensional Granular Environment

The drag of two cylindrical intruders in a two-dimensional granular environment is numerically studied by the discrete element method. We find the yield force, below which the intruders cannot move because of interactions with the surrounding particles. Above the yield force, on the other hand, the intruders can move at a constant speed. We investigate the relationship between the drag force and the steady speed of the intruders, where the speed becomes higher as the distance between the intruders decreases. We confirm that the origin of the yield is the Coulombic friction between the particles and the bottom plate by changing the value of the friction coefficient. We also find that the yield force is almost proportional to the friction coefficient, which means that the number of particles determining the yield force is almost constant. On the other hand, the two-dimensional elasticity is applicable to determine the stress fields around the intruders. We confirm that fields asymmetric with respect to the drag direction are reproduced by using the information of the stresses on the surfaces of the intruders by introducing bipolar coordinates.

cond-mat.soft↗

arXiv2021

Impact of Softness of Particles on Rheology of Dilute Granular Gases

We numerically and theoretically investigate how the softness of particles affects the rheology of sheared dilute granular gases. We find that the kinetic theory predicts the deviation of the flow curve from the Bagnold scaling, and it works well below a certain shear rate when we compare with the simulation results. It is also found that there is no theoretical solution above this shear rate, which is because the energy loss due to inelastic collisions cannot be balanced with the energy injection by the shear.

cond-mat.soft↗

arXiv2021

Mpemba effect in inertial suspensions

The Mpemba effect (a counterintuitive thermal relaxation process where an initially hotter system may cool down to the steady state sooner than an initially colder system) is studied in terms of a model of inertial suspensions under shear. The relaxation to a common steady state of a suspension initially prepared in a quasi-equilibrium state is compared with that of a suspension initially prepared in a nonequilibrium sheared state. Two classes of Mpemba effect are identified, the normal and the anomalous one. The former is generic, in the sense that the kinetic temperature starting from a cold nonequilibrium sheared state is overtaken by the one starting from a hot quasi-equilibrium state, due to the absence of initial viscous heating in the latter, resulting in a faster initial cooling. The anomalous Mpemba effect is opposite to the normal one since, despite the initial slower cooling of the nonequilibrium sheared state, it can eventually overtake an initially colder quasi-equilibrium state. The theoretical results based on kinetic theory agree with those obtained from event-driven simulations for inelastic hard spheres. It is also confirmed the existence of the inverse Mpemba effect, which is a peculiar heating process, in these suspensions. More particularly, we find the existence of a mixed process in which both heating and cooling can be observed during relaxation.

cond-mat.stat-mech↗

arXiv2020

Two-Step Discontinuous Shear Thickening of Dilute Inertial Suspensions Having Soft-Core Potential

Kinetic theory for dilute inertial suspension having soft-core potential is theoretically investigated. From the analysis of the scattering process, the expression of the scattering angle is analytically obtained. We derive the flow curve between the viscosity and the shear rate, which shows two-step discontinuous shear thickening when we change the softness of the particles. The molecular dynamics simulation shows that our theoretical results are consistent with the numerical ones.

cond-mat.soft↗

arXiv2020

Particle flows around an intruder

Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be reproduced by a simple analysis of a collision model between the intruder and particle flows. The crossover from Epstein's law to Stokes' law is also found for the low-speed regime as the time evolution of the drag force caused by beam particles. We also show the existence of turbulent-like behavior of the particle flows behind the intruder with the aid of the second invariant of the velocity gradient tensor and the relative mean square displacement for the high-speed regime and a large intruder.

cond-mat.soft↗

arXiv2020

Enskog kinetic theory of rheology for a moderately dense inertial suspension

The Enskog kinetic theory for moderately dense inertial suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the background fluid on suspended particles is modeled via a viscous drag force plus a Langevin-like term defined in terms of the background temperature. In a previous paper [Hayakawa et al., Phys. Rev. E 96, 042903 (2017)], Grad's moment method with the aid of a linear shear-rate expansion was employed to obtain a theory which gave good agreement with the results of event-driven Langevin simulations of hard spheres for low densities and/or small shear rates. Nevertheless, the previous approach had a limitation of applicability to the high shear-rate and high density regime. Thus, in the present paper, we extend the previous work and develop Grad's theory including higher order terms in the shear rate. This improves significantly the theoretical predictions, a quantitative agreement between theory and simulation being found in the high-density region (volume fractions smaller than or equal to $0.4$).

cond-mat.stat-mech↗

arXiv2020

Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening

The Enskog kinetic theory for moderately dense gas-solid suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the environmental fluid on solid particles is modeled via a viscous drag force plus a stochastic Langevin-like term. The Enskog equation is solved by means of two independent but complementary routes: (i) Grad's moment method and (ii) event-driven Langevin simulation of hard spheres. Both approaches clearly show that the flow curve (stress-strain rate relation) depends significantly on the volume fraction of the solid particles. In particular, as the density increases, there is a transition from the discontinuous shear thickening (observed in dilute gases) to the continuous shear thickening for denser systems. The comparison between theory and simulations indicate that while the theoretical predictions for the kinetic temperature agree well with simulations for densities $φ\lesssim 0.5$, the agreement for the other rheological quantities (the viscosity, the stress ratio and the normal stress differences) is limited to more moderate densities ($φ\lesssim 0.3$) if the inelasticity during collisions between particles is not large. [This paper has been published in Phys. Rev. E {\bf 96}, 42903 (2017) but we have realized that there are some typos and mistakes after its publication. So we add the Erratum which will be published in PRE in the top of this paper.]

cond-mat.stat-mech↗

arXiv2020

Scaling law of the drag force in dense granular media

Making use of the system of pulling a spherical intruder in static three-dimensional granular media, we numerically study the scaling law for the drag force $F_{\rm drag}$ acting on the moving intruder under the influence of the gravity. Suppose if the intruder of diameter $D$ immersed in a granular medium consisting of grains of average diameter $d$ is located at a depth $h$ and moves with a speed $V$, we find that $F_{\rm drag}$ can be scaled as $(D+d)^{ϕ_μ} h^{α_μ}$ with two exponents $ϕ_μ$ and $α_μ$, which depend on the friction coefficient $μ$ and satisfy an approximate sum rule $ϕ_μ+α_μ\approx 3$. This scaling law is valid for the arbitrary Froude number (defined by $\mathrm{Fr}={2 V}\sqrt{{2D}/{g}}\big/(D+d)$), if $h$ is sufficiently deep. We also identify the existence of three regimes (quasistatic, linear, and quadratic) at least for frictional grains in the velocity dependence of drag force. The crossovers take place at $\mathrm{Fr}\approx 1$ between the quasistatic to the linear regimes and at $\mathrm{Fr}\approx 5$ between the linear to the quadratic regimes. We also observe that Froude numbers at which these crossovers between the regimes happen are independent of the depth $h$ and the diameter of the intruder $D$. We also report the numerical results on the average coordination number of the intruder and average contact angle as functions of intruder velocity.

cond-mat.soft↗

arXiv2019

Drag acting on an intruder in a three-dimensional granular environment

The drag acting on an intruder in a three-dimensional frictionless dry granular environment is numerically studied. It is found the followings: (i) There is no yield force for the motion of the intruder without the gravity. (ii) The drag is proportional to the cross section of the moving intruder. (iii) If the intruder is larger than surrounding grains, the drag is proportional to the moving speed $V$ of the intruder for dense systems, but it exhibits a crossover from quadratic to linear dependences of the moving speed when the volume fraction of the surrounding grains is much lower than the jamming point. (iv) There is a plateau regime where the drag is almost independent of $V$ if the size of the intruder is identical to those of the environmental grains and the volume fraction is near the jamming point.

cond-mat.soft↗

arXiv2019

Ground state modulations in the ${\mathbb C}P^{N-1}$ model

In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional ${\mathbb C}P^{N-1}$ model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations.

hep-th↗

arXiv2019

Casimir Force for the ${\mathbb C}P^{N-1}$ Model

In this work, we derive exact self-consistent solutions to the gap equations of the $\mathbb{C}P^{N-1}$ model on a finite interval with Dirichlet boundary conditions in the large-$N$ approximation. The solution reproduce the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.

hep-th↗

arXiv2019

Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

A kinetic theory for a dilute gas-solid suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curve (stress-strain rate relation) has a S-shape as a crossover from the Newtonian to the Bagnoldian for a granular suspension or from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles. The existence of the S-shape in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The simulation confirms that the DST takes place in the linearly unstable region of the uniformly sheared state.

cond-mat.stat-mech↗