Supercooled liquids analogous fractional Stokes–Einstein relation in NaCl solution above room temperature

The Stokes–Einstein relation D～T/η and its two variants D～τ~(-1) and D～T/τ follow a fractional form in supercooled liquids, where D is the diffusion constant, T the temperature, η the shear viscosity, and τ the structural relaxation time.The fractional Stokes–Einstein relation is proposed to result from the dynamic heterogeneity of supercooled liquids.In this work, by performing molecular dynamics simulations, we show that the analogous fractional form also exists in sodium chloride(NaCl) solutions above room temperature.D～τ~(-1) takes a fractional form within 300–800 K; a crossover is observed in both D～T/τ and D～T/η.Both D～T/τ and D～T/η are valid below the crossover temperature T_x,but take a fractional form for T T_x.Our results indicate that the fractional Stokes–Einstein relation not only exists in supercooled liquids but also exists in NaCl solutions at high enough temperatures far away from the glass transition point.We propose that D～T/η and its two variants should be critically evaluated to test the validity of the Stokes–Einstein relation.     

Fractional variant of Stokes–Einstein relation in aqueous ionic solutions under external static electric fields

Both ionic solutions under an external applied static electric field E and glassy-forming liquids under undercooled state are in non-equilibrium state.In this work,molecular dynamics(MD)simulations with three aqueous alkali ion chloride(NaCl,KCl,and RbCl)ionic solutions are performed to exploit whether the glass-forming liquid analogous fractional variant of the Stokes–Einstein relation also exists in ionic solutions under E.Our results indicate that the diffusion constant decouples from the structural relaxation time under E,and a fractional variant of the Stokes–Einstein relation is observed as well as a crossover analogous to the glass-forming liquids under cooling.The fractional variant of the Stokes–Einstein relation is attributed to the E introduced deviations from Gaussian and the nonlinear effect.     

Revisiting the breakdown of Stokes-Einstein relation in glass-forming liquids with machine learning

The Stokes-Einstein(SE) relation has been considered as one of the hallmarks of dynamics in liquids. It describes that the diffusion constant D is proportional to(τ/T)~(–1), where τ is the structural relaxation time and T is the temperature. In many glassforming liquids, the breakdown of SE relation often occurred when the dynamics of the liquids becomes glassy, and its origin is still debated among many scientists. Using molecular dynamics simulations and support-vector machine method, it is found that the scaling between diffusion and relaxation fails when the total population of solid-like clusters shrinks at the maximal rate with decreasing temperature, which implies a dramatic unification of clusters into an extensive dominant one occurs at the time of breakdown of the SE relation. Our data leads to an interpretation that the SE violation in metallic glass-forming liquids can be attributed to a specific change in the atomic structures.     

Measurement scheme to detect α relaxation time of glass-forming liquid

A measurement scheme for detecting the α relaxation time(τ) of glass-forming liquid is proposed, which is based on the measured ionic conductivity of the liquid doped with probing ions by low-and middle-frequency dielectric spectroscopy and according to the Nernst–Einstein, Stokes–Einstein, and Maxwell equations. The obtained τ values of glycerol and propylene carbonate by the scheme are consistent with those obtained by traditional dielectric spectroscopy, which confirms its reliability and accuracy. Moreover, the τ of 1,2-propanediol in a larger temperature range is compared with existing data.     

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

The current–phase relations of a ring-trapped Bose–Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current–phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current–phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current–phase relation is given by investigating the behavior of soliton solution.     

Scaling Law of Exponents in Cosmological Clustering

The density of N-clusters(the clusters which contain N galaxies)in the Universe is shown from observations to scale with N as nN ∝ N^-τ with τ=3/γ 1 and the correlation exponent γ≈1.8.Correspondingly,a acaling relation τ=29-9γ/12-4γ between the two exponents,which agrees with the observations,is found analytically in our naive clustering model.     

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb–Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb–Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter α = 1-2/γ, where γ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb–Liniger model in terms of the fractional statistical parameter.     

Neutrino mixing matrix and masses from a particular two-zero texture based on A4 symmetry

The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A₄ symmetry,where charged lepton mass matrix is diagonal.The texture is ■ with(μ,μ) and(τ,τ) vanishing element of the neutrino mass matrix.The texture ■ has magic and μ-τ symmetry,with a tribimaximal form of the mixing matrix,which leads to θ₁₃=0 that it is not consistent with experimental data and at first,does not seem to be allowed.Since θ₁₃ a sma...     

Boron diffusion in bcc-Fe studied by first-principles calculations

The diffusion mechanism of boron in bcc-Fe has been studied by first-principles calculations. The diffusion coefficients of the interstitial mechanism, the B–monovacancy complex mechanism, and the B–divacancy complex mechanism have been calculated. The calculated diffusion coefficient of the interstitial mechanism is D_0= 1.05 ×10~(-7)exp(-0.75 e V/k T) m~2· s~(-1), while the diffusion coefficients of the B–monovacancy and the B–divacancy complex mechanisms are D_1= 1.22 × 10~(-6)f1exp(-2.27 e V/k T) m~2· s~(-1)and D_2≈ 8.36 × 10~(-6)exp(-4.81 e V/k T) m~2· s~(-1), respectively. The results indicate that the dominant diffusion mechanism in bcc-Fe is the interstitial mechanism through an octahedral interstitial site instead of the complex mechanism. The calculated diffusion coefficient is in accordance with the reported experiment results measured in Fe–3%Si–B alloy(bcc structure). Since the non-equilibrium segregation of boron is based on the diffusion of the complexes as suggested by the theory, our calculation reasonably explains why the non-equilibrium segregation of boron is not observed in bcc-Fe in experiments.     

Information Measure for Size Distribution of Avalanches in the Bak—Sneppen Evolution Model

Information of avalanche size distribution is measured by calculating information entropy(IE) in the BakSneppen evolution model.It is found that the IE increases as the model evolves,Specifically,we establish the relation between the IE and the self-oprganized threshold fc.The variation of the IE near the critical point yields an exponent entropy index E=(τ-1)/σ，where τand σ prepresent the critical exponents for avalanche size distribution and avalanche size cutoff,respectively,A new quantity Dτ(g)(g=1-(fc-G)^τ-1)/σ,where G is the gap of the current state),defined as 1-Iτ(g)/Iτ(1),with Iτ(g) and Iτ(1)being the IE for the current state and the critical one respectively,is suggested that it represents the distance between the state with gap G and the critical one.     

Dark Soliton Solutions of Space-Time Fractional Sharma–Tasso–Olver and Potential Kadomtsev–Petviashvili Equations

Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.     

Potential-Dependent Generalized Einstein Relation in Disordered Organic Semiconductors

The generalized Einstein relation （GER） is extended to consider the potential energy of carriers in an electric field （PDGER）. It can be equivalently seen as the GER having position-dependent Fermi energy, and implies the organic semiconductor is in non-equilibrium under an electric field. The distribution of the carrier density with position is solved for two polymer layers. The numerical results are used to evaluate the PDGER. It is shown that the ratio of diffusion coefficient to mobility,μ/D, increases with Fermi energy and decreases with carrier density. The PDGER gives non-traditional values for the two polymer layers; the value of μ/D is small near the surface, and slightly increases as the position departs from the surface.     

Critical behavior in the layered organic–inorganic hybrid(CH_3NH_3)_2CuCl_4

The critical properties and the nature of the ferromagnetic–paramagnetic phase transition in the 2D organic-inorganic hybrid(CH_3NH_3)_2 CuCl_4 single crystal have been investigated by dc magnetization in the vicinity of the magnetic transition. Different techniques were used to estimate the critical exponents near the ferromagnetic–paramagnetic phase transition such as modified Arrott plots, the Kouvel–Fisher method, and the scaling hypothesis. Values of β = 0.22, γ = 0.82, and δ = 4.4 were obtained. These critical exponents are in line with their corresponding values confirmed through the scaling hypothesis as well as the Widom scaling relation, supporting their reliability. It is concluded that this 2D hybrid compound possesses strong ferromagnetic intra-layer exchange interaction as well as weak interlayer ferromagnetic coupling that causes a crossover from 2D to 3D long-range interaction.     

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate are investigated by using the Hartree–Fock–Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements.According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.     

Simple Analytic Expression with High Precision for the Barker—Henderson Diameter

A fitting procedure is proposed to establish two analytic aproximate expressions for the complicated Barker-Henderson(BH) diameter with Lennard-Jones potential in two temperature ranges.Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of internal energy.we propose to fit the derivative directly,instead of usually fitting the original function and subsequently deriving its derivative.The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature.The one with following form only has an average fitting 0.0063% in the reduced temperature range(0.4≤κT/ε≤15).and can be extrapolated to a wider temperature range (0.4≤κT/ε≤50)with an average orror 0.13%,which is d/σ=1.1755 0.02878lnτ-0.2072τ^1/4 0.00463τ^3/4.     

Abnormal breakdown of Stokes–Einstein relation in liquid aluminium

We present the results of systematic molecular dynamics simulations of pure aluminium melt with a well-accepted embedded atom potential. The structure and dynamics were calculated over a wide temperature range, and the calculated results(including the pair correlation function, self-diffusion coefficient, and viscosity) agree well with the available experimental observations. The calculated data were used to examine the Stokes–Einstein relation(SER). The results indicate that the SER begins to break down at a temperature T_x(~1090 K) which is well above the equilibrium melting point(912.5 K).This high-temperature breakdown is confirmed by the evolution of dynamics heterogeneity, which is characterised by the non-Gaussian parameter α_2(t). The maximum value of α 2(t), α_(2,max), increases at an accelerating rate as the temperature falls below Tx. The development of α_(2,max) was found to be related to the liquid structure change evidenced by local fivefold symmetry. Accordingly, we suggest that this high-temperature breakdown of SER has a structural origin. The results of this study are expected to make researchers reconsider the applicability of SER and promote greater understanding of the relationship between dynamics and structure.     

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose–Einstein condensates with axisymmetric configurations in the R2×S1space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional(3D) skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross–Pitaevskii equations in imaginary time.     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.     

Magnetic impurity in hybrid and type-Ⅱ nodal line semimetals

We study the Kondo screening of a spin-1/2 magnetic impurity in the hybrid nodal line semimetals(NLSMs) and the type-Ⅱ NLSMs by using the variational method. We mainly study the binding energy and the spin–spin correlation between magnetic impurity and conduction electrons. We find that in both the hybrid and type-Ⅱ cases, the density of states(DOS) is always finite, so the impurity and the conduction electrons always form bound states, and the bound state is more easily formed when the DOS is large. Meanwhile, due to the unique dispersion relation and the spin–orbit couplings in the NLSMs, the spatial spin–spin correlation components show very interesting features. Most saliently, various components of the spatial spin–spin correlation function decay with 1/r~2 in the hybrid NLSMs, while they follow 1/r~3 decay in the type-Ⅱ NLSMs. This property is mainly caused by the special band structures in the NLSMs, and it can work as a fingerprint to distinguish the two types of NLSMs.