New exact solutions toN-dimensional radially symmetric nonlinear diffusion equations

New exact solutions toN-dimensional radially symmetric nonlinear diffusion equations with power-law diffusivities are constructed in terms of the generalized conditional symmetry method, which can be thought as a generalization of the nonclassical symmetry method due to Bluman and Cole.     

Directed motion for delta-kicked atoms with broken symmetries: comparison between theory and experiment

We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.     

First-principles study of lithium-ion diffusion in β-Li3PS4 for solid-state electrolytes

Understanding the role of partially occupied sites in Li-based superionic conductors is key to improving performance of solid-state electrolyte materials. We study the optimized structure of crystalline β-Li₃PS₄ and the Li-ion diffusion using first-principles calculations and the nudged elastic band method. Considering diffusion paths through both interstitial and vacancy exchanges, we calculate the migration energies of Li ions. We find that the phonon-mode softening and concurrent inversion symmetry breaking leads to a more stable structure with low symmetry. Atomic distortion from the phonon softening provides diffusion paths for Li ions with less migration energies than the ones in high-symmetry structures. Our results show that diffusion of Li ion is highly anisotropic through the armchair- or zigzag-shaped channels along the b-axis that contain Li-ion sites with fractional occupation.     

Effects of bulk diffusion on interfacial dynamics

We study the influence of bulk diffusion on the dynamics of an interface in the two-phase region of two component systems. We establish a set of equations of motion describing capillary waves and their coupling to a slow diffusion mode in the bulk. Valid for the general case of density dependent bulk diffusion coefficients, these equations are both non-local and non-linear. The nonlinearity is a realization of the full Galilean symmetry associated with the system. Studying the dispersion relations for the linear regime, we find a significant difference between systems with Ising symmetry and those without.     

Separation of variables in the diffusion equation. I

For both stationary and nonstationary cases, all the coefficients of the linear diffusion equation with a constant diffusion tensor are enumerated for which total separation of the variables is possible by means of differential symmetry operators of a definite structure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 46–53, November, 1976.     

Rotational symmetry breaking in small-area circular vertical cavity surface emitting lasers

We investigate theoretically the dynamics of three low-order transverse modes in a small-area vertical cavity surface emitting laser. We demonstrate the spontaneous breaking of axial symmetry of the transverse field distribution in such a device. In particular, we show that if the linewidth enhancement factor is sufficiently large dynamical regimes with broken axial symmetry can exist up to very high diffusion coefficients ~ 10 μm²/ns.     

NO adsorption and diffusion on unreconstructed Pt{1 0 0} surface. A density functional theory investigation

Ab initio density functional theory was used to investigate the adsorption and diffusion of a single NO molecule on the unreconstructed Pt{1 0 0}-(1 × 1) surface. To our knowledge this is the first theoretical study of the NO diffusion activation energy on the Pt{1 0 0} surface. The most stable adsorption position for NO corresponds to the bridge site with the axis of the molecule perpendicular to the surface. The bond of the NO molecule to the surface is through the N-atom. We found that there is a low adsorption energy when the NO molecule is bonded through the O-atom and the axis is perpendicular to the surface, for the three high symmetry sites investigated. NO diffusion between bridge-hollow sites, bridge-atop sites, and hollow-atop sites was also investigated. The barrier for NO diffusion is 0.41 eV, which corresponds to the energy difference between the bridge and hollow sites. This value is around 15% of the highest adsorption energy found on this surface. NO stretch frequencies are also calculated for the three high symmetry sites investigated.     

Similarity Reductions for a Nonlinear Diffusion Equation

Abstract

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method.     

Progress towards determining the density dependence of the nuclear symmetry energy using heavy-ion reactions

The latest development in determining the density dependence of the nuclear symmetry energy using heavy-ion collisions is reviewed. Within the IBUU04 version of an isospin- and momentum-dependent transport model using a modified Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are found to be consistent with a nuclear symmetry energy of E _sym(ρ)≈31.6(ρ/ρ₀)^1.05 at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made.     

Probing the nuclear symmetry energy with heavy-ion reactions induced by neutron-rich nuclei

Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretical progress on probing the high density behaviors of the nuclear symmetry energy in heavy-ion reactions induced by high energy radioactive beams.      

Symmetry of Equations with Convection Terms

Abstract

We study symmetry properties of the heat equation with convection term (the equation of convection diffusion) and the Schrödinger equation with convection term. We also investigate the symmetry of systems of these equations with additional conditions for potentials. The obtained results are applied to construction of exact solutions of the system of the Schrödinger equation with convection term and the Euler equations for potentials.     

Phase transition in the scalar noise model of collective motion in three dimensions

We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case [CITE]. For small velocity (v≤0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to a boundary condition dependent symmetry breaking of the solutions.     

Effective diffusion coefficient for two-dimensional,periodic channels

A Green's function method has been used to calculate the first-passage time for traveling a fixed distance in a two-dimensional space with periodic walls. The results are used to find the effective diffusion coefficient for the space. Application to three-dimensional spaces with cylindrical symmetry and periodic walls is outlined.     

Results for a fractional diffusion equation with a nonlocal term in spherical symmetry

We obtain time dependent solutions for a fractional diffusion equation containing a nonlocal term by considering the spherical symmetry and using the Green function approach. The nonlocal term incorporated in the diffusion equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution. In addition, a rich class of anomalous diffusion processes may be described from the results obtained here.     

Diffusion of hydrogen in Pd assisted by inelastic ballistic hot electrons

Sykes et al. [Proc. Natl. Acad. Sci. U.S.A. 102, 17907 (2005)] have reported how electrons injected from a scanning tunneling microscope modify the diffusion rates of H buried beneath Pd(111). A key point in that experiment is the symmetry between positive and negative voltages for H extraction, which is difficult to explain in view of the large asymmetry in Pd between the electron and hole densities of states. Combining concepts from the theory of ballistic electron microscopy and electron-phonon scattering we show that H diffusion is driven by the s-band electrons only, which explains the observed symmetry.     

Effects of isospin and momentum dependent interactions on liquid–gas phase transition in hot asymmetric nuclear matter

The liquid–gas phase transition in hot neutron-rich nuclear matter is investigated within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, a momentum-independent interaction (MID), and an isoscalar momentum-dependent interaction (eMDYI). The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy with a softer symmetry energy giving a higher critical pressure and a larger area of phase-coexistence region. Compared with the momentum-independent MID interaction, the isospin and momentum-dependent MDI interaction is found to increase the critical pressure and enlarge the area of phase-coexistence region. For the isoscalar momentum-dependent eMDYI interaction, a limiting pressure above which the liquid–gas phase transition cannot take place has been found and it is shown to be sensitive to the stiffness of the symmetry energy.     

Determination of the stiffness of the nuclear symmetry energy from isospin diffusion

With an isospin- and momentum-dependent transport model, we find that the degree of isospin diffusion in heavy-ion collisions at intermediate energies is affected by both the stiffness of the nuclear symmetry energy and the momentum dependence of the nucleon potential. Using a momentum dependence derived from the Gogny effective interaction, recent experimental data from NSCL-MSU on isospin diffusion are shown to be consistent with a nuclear symmetry energy given by E(sym)(rho) approximately 31.6(rho/rho(0))(1.05) at subnormal densities. This leads to a significantly constrained value of about -550 MeV for the isospin-dependent part of the isobaric incompressibility of isospin asymmetric nuclear matter.     

Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice

We investigate the dynamics of a particle on a periodic lattice, coupled to phonons with ohmic dissipation. At T = 0 a symmetry breaking appears, which corresponds to a transition between a localized and a delocalized regime. For T > 0 we recover a diffusive motion for which the diffusion coefficient is computed.     

Theoretical description of the methyl group relaxation in liquids

Spin-lattice and spin-spin relaxation times of protons and deuterons of methyl groups in liquids are calculated using a semiclassical form of the density operator formalism and symmetry adapted spherical tensors. The model of molecular motion assumes diffusion of the whole molecule containing the methyl group with some internal rotation. Special consideration is given to uniaxial internal rotation and anisotropic diffusion as well as to biaxial internal rotation and isotropic diffusion in interpreting the experimental results.