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The magnetic field dependences of the critical-current of a granular s-wave superconductor has been determined by considering the rectangular and circular junction model of an array of small superconducting particles which interacting by Josephson coupling through insulating barriers. We will show that in the case of circular model, the maximum critical current of the Josephson current is larger than that of rectangular model., Comment: 7 pages, 5 figuares

By using two-fluid model the effect of impurities on the transition temperature of a dipolar trapped Bose gas is investigated. By treating Gaussian spatial correlation for impurities from the interaction modified spectra of the system, the formula for the shift of transition temperature is derived. The shift of the transition temperature contains essentially three contributions due to contact, dipole-dipole and impurity interactions. Applying our results to Dipolar Bose gases show that the shift of the transition temperature due to impurities could be measured for isotropic trap (dipole-dipole contributions is zero) and Feshbach resonance technique (contact potential contribution is negligible)., Comment: 12 pages. arXiv admin note: text overlap with arXiv:cond-mat/9911278, arXiv:cond-mat/0606569, arXiv:cond-mat/9903029 by other authors

The superconducting reservoir effect on the current carrying transport of a double quantum dot in Markovian regime is investigated. For this purpose, a quantum master equation (QME) at finite temperature is derived for the many-body density matrix of an open quantum system. The dynamics and the steady-state properties of the double quantum dot system for arbitrary bias are studied. We will show that how the populations and coherencies of the system states are affected by superconducting leads. The energy parameter of system contains essentially four contributions due to dots system-electrodes coupling, intra dot coupling, two quantum dots inter coupling and superconducting gap. The coupling effect of each energy contribution is applied to currents and coherencies results. In addition, the effect of energy gap is studied by considering the amplitude and lifetime of coherencies to get more current through the system., Comment: 14 pages, 7 figuares. arXiv admin note: text overlap with arXiv:cond-mat/0610004 by other authors

The twist angle {\gamma} dependence of the Josephson critical current of d-wave superconductors in one junction and a granular system is considered. Our results show that the twist angle {\gamma} dependence of the d-wave Josephson critical current is the same for one junction and a granular system. The magnetic field dependences of the critical-current of a granular d-wave superconductor has also been determined by considering the rectangular and circular junction model of an array of small superconducting particles which interacting by Josephson coupling through insulating barriers. We will show that in the case of circular model, the critical current of the Josephson current is larger than that of rectangular one., Comment: 14 pages,6 figuares. arXiv admin note: text overlap with arXiv:cond-mat/0603522, arXiv:cond-mat/9411104 by other authors

In this paper, the exact vacuum solution of a general plane symmetric spacetime is investigated in metric f(R) gravity with the assumption of constant Ricci scalar. For this solution, we have studied the generalized Landau-Lifshitz energy-momentum complex in this theory to determine the energy distribution expressions for some specific f(R) models. Also, we show that these models satisfy the constant curvature condition.

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker-Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule's parameters on the cooling mechanism is studied., Comment: 10 pages, 8 figures

We study some differential complexes in continuum mechanics that involve both symmetric and non-symmetric second-order tensors. In particular, we show that the tensorial analogue of the standard grad-curl-div complex can simultaneously describe the kinematics and the kinetics of motions of a continuum. The relation between this complex and the de Rham complex allows one to readily derive the necessary and sufficient conditions for the compatibility of the displacement gradient and the existence of stress functions on non-contractible bodies. We also derive the local compatibility equations in terms of the Green deformation tensor for motions of $2$D and $3$D bodies, and shells in curved ambient spaces with constant curvatures.

We report the results of the Ni-based bulk metallic glass structural evolution and crystallization behavior in situ investigation. The X-ray diffraction (XRD), transmission electron microscopy (TEM), nano-beam diffraction (NBD), differential scanning calorimetry (DSC), radial distribution function (RDF) and scanning probe microscopy/spectroscopy (STM/STS) techniques were applied to analyze the structure and electronic properties of Ni63.5Nb36.5 glasses before and after crystallization. It was proved that partial surface crystallization of Ni63.5Nb36.5 can occur at the temperature lower than for the full sample crystallization. According to our STM measurements the primary crystallization is originally starting with the Ni3Nb phase formation. It was shown that surface crystallization drastically differs from the bulk crystallization due to the possible surface reconstruction. The mechanism of Ni63.5Nb36.5 glass alloy 2D-crystallization was suggested, which corresponds to the local metastable (3x3)-Ni(111) surface phase formation. The possibility of different surface nano-structures development by the annealing of the originally glassy alloy in ultra high vacuum at the temperature lower, than the crystallization temperature was shown. The increase of mean square surface roughness parameter Rq while moving from glassy to fully crystallized state can be caused by concurrent growth of Ni3Nb and Ni6Nb7 bulk phases. The simple empirical model for the estimation of Ni63.5Nb36.5 cluster size was suggested, and the obtained values (7.64 A, 8.08 A) are in good agreement with STM measurements data (8 A-10 A).

A rigorous proof for convergence of the Wolf method for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method converges to the one obtained via Ewald method.

We impose uniform electric fields both parallel and normal to 180^o ferroelectric domain walls in PbTiO_3 and obtain the equilibrium structures using the method of anharmonic lattice statics. In addition to Ti-centered and Pb-centered perfect domain walls, we also consider Ti-centered domain walls with oxygen vacancies. We observe that electric field can increase the thickness of the domain wall considerably. We also observe that increasing the magnitude of electric field we reach a critical electric field E^c; for E > E^c there is no local equilibrium configuration. Therefore, E^c can be considered as an estimate of the threshold field E_h for domain wall motion. Our numerical results show that Oxygen vacancies decrease the value of E^c. As the defective domain walls are thicker than perfect walls, this result is in agreement with the recent experimental observations and continuum calculations that show thicker domain walls have lower threshold fields.

Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180^o ferroelectric domain walls (DW) in PbTiO_3. We consider three different types of steps: i) Ti-Ti step that joins a Ti-centered DW to a Ti-centered DW, (ii) Pb-Pb step that joins a Pb-centered DW to a Pb-centered DW, and (iii) Pb-Ti step that joins a Pb-centered DW to a Ti-centered DW. We show that atomic distortions due to these steps broaden a DW but are localized, i.e., they are confined to regions with dimensions of a few lattice spacings. We see that a step locally thickens the domain wall; the defective domain wall is two to three times thicker than the perfect domain wall depending on the step type. We also observe that steps distort the polarization distribution in a mixed Bloch-N\'{e}el like way; polarization rotates out of the domain wall plane near the steps. Our calculations show that Pb-Pb steps have the lowest static energy.

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a quasiharmonic lattice dynamics approach to approximate the free energy. Finally, the defect structure at a finite temperature is obtained by minimizing the approximate Helmholtz free energy. For higher temperatures we take the relaxed configuration at a lower temperature as the reference configuration. This method can be used to semi-analytically study the structure of defects at low but non-zero temperatures, where molecular dynamics cannot be used. As an example, we obtain the finite temperature structure of two 180^o domain walls in a 2-D lattice of interacting dipoles. We dynamically relax both the position and polarization vectors. In particular, we show that increasing temperature the domain wall thicknesses increase.

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.

In this letter we obtain the finite-temperature structure of 180^o domain walls in PbTiO3 using a quasi-harmonic lattice dynamics approach. We obtain the temperature dependence of the atomic structure of domain walls from 0K up to room temperature. We also show that both Pb-centered and Ti-centered 180^o domain walls are thicker at room temperature; domain wall thickness at T=300K is about three times larger than that of T=0K. Our calculations show that Ti-centered domain walls have a lower free energy than Pb-centered domain walls and hence are more likely to be seen at finite temperatures.

In this paper we study the effect of normal and shear strains and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3. It is known that oxygen vacancies move to the domain walls and pin them. Hence, we assume a periodic arrangement of oxygen vacancies on both Pb-centered and Ti-centered domain walls in PbTiO_3. We use a semi-analytic anharmonic lattice statics method for obtaining the relaxed configurations using a shell potential. In agreement with recent ab initio calculations, we observe that a Pb-centered domain wall with oxygen vacancies is not stable even under strain. Our semi-analytic calculations for PbTiO_3 show that oxygen vacancies affect the structure of 180^o domain walls significantly but do not have a considerable effect on the thickness of domain walls; they broaden the domain walls by about fifty percent. We also study the effect of normal and shear strains on both perfect and defective 180^o domain walls. We observe that normal and shear strains affect the structure but do not change the domain wall thickness.

In this paper we formulate a geometric theory of thermal stresses. Given a temperature distribution, we associate a Riemannian material manifold to the body, with a metric that explicitly depends on the temperature distribution. A change of temperature corresponds to a change of the material metric. In this sense, a temperature change is a concrete example of the so-called referential evolutions. We also make a concrete connection between our geometric point of view and the multiplicative decomposition of deformation gradient into thermal and elastic parts. We study the stress-free temperature distributions of the finite-deformation theory using curvature tensor of the material manifold. We find the zero-stress temperature distributions in nonlinear elasticity. Given an equilibrium configuration, we show that a change of the material manifold, i.e. a change of the material metric will change the equilibrium configuration. In the case of a temperature change, this means that given an equilibrium configuration for a given temperature distribution, a change of temperature will change the equilibrium configuration. We obtain the explicit form of the governing partial differential equations for this equilibrium change. We also show that geometric linearization of the present nonlinear theory leads to governing equations that are identical to those of the classical linear theory of thermal stresses.

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show that time dependency of material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange-d'Alembert's principle with Rayleigh's dissipation functions to derive all the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of deformation gradient $\mathbf{F}=\mathbf{F}_e\mathbf{F}_g$ into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas.