We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observabl...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.
Based on a series of supercell density functional calculations of Fe-doped TiO2 both with and without O vacancy (VO), we show that VO plays an important role in determining the magnetic properties of the dilute magnet...
Based on a series of supercell density functional calculations of Fe-doped TiO2 both with and without O vacancy (VO), we show that VO plays an important role in determining the magnetic properties of the dilute magnetic semiconductors (DMS). Without VO, two Fe atoms in rutile lattice are ferromagnetically coupled except at a separation distance of 3.57Å, where they are antiferromagnetically coupled. The VO introduces two electrons into the conduction bands of rutile, which are either captured by the Fe dopants or form a shallow impurity state. The ferromagnetic (FM) coupling J between two Fe atoms is enhanced, through the enhancement of the FM double exchange if VO is sufficiently close.
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implement...
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.
The conventional definition of spin current is incomplete and unphysical in describing spin transport in systems with spin-orbit coupling. A proper and measurable spin current is established in this study, which fits ...
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The conventional definition of spin current is incomplete and unphysical in describing spin transport in systems with spin-orbit coupling. A proper and measurable spin current is established in this study, which fits well into the standard framework of near-equilibrium transport theory and has the desirable property to vanish in insulators with localized orbitals. Experimental implications of our theory are discussed.
A one-dimensional network on which there are long-range bonds at lattice distances l>1 with the probability P(l)∝l−δ has been taken under consideration. We investigate the critical behavior of the Ising model on ...
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A one-dimensional network on which there are long-range bonds at lattice distances l>1 with the probability P(l)∝l−δ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbors apart from their nearest neighbors for 0⩽δ<2. It is observed that there is a finite temperature phase transition in the entire range. For 0⩽δ<1, finite-size scaling behavior of various quantities are consistent with mean-field exponents while for 1⩽δ⩽2, the exponents depend on δ. The results are discussed in the context of earlier observations on the topology of the underlying network.
The full-charge-density screened Korringa-Kohn-Rostoker method is described and applied to calculate bulk and surface energies of transition metals. It is demonstrated that due to a truncated angular momentum expansio...
The full-charge-density screened Korringa-Kohn-Rostoker method is described and applied to calculate bulk and surface energies of transition metals. It is demonstrated that due to a truncated angular momentum expansion of the shape functions, the otherwise ultimate freedom of adding a constant to the potential in all space leads, in particular close to the cell boundaries, to potentials of fairly different shapes. Thus a dependence on this constant potential shift emerges for the calculated bulk total energies, equilibrium volumes, and bulk moduli, as well as for the surface energies and the work functions. A reasonable choice for the constant shift seems to set the bulk potential at the muffin-tin radius to zero. By making this choice the calculations give results that are in very good agreement to those calculated by other full-charge-density or full-potential methods.
A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed ato...
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A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.
We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing ...
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We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be ϕMRJ≈0.46, 0.31, and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form ϕMRJ=c1∕2d+(c2d)∕2d, where c1=−2.72 and c2=2.56, which appears to be consistent with the high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function g2(r) and structure factor S(k) for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed “decorrelation principle,” which, among other things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit d→∞. As in three dimensions (where ϕMRJ≈0.64), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in g2(r) at contact with power-law exponent ≈0.4. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where g2(r) has its first minimum. Additionally, we obtain estimates for the freezing and melting packing fractions for the equilibrium hard-sphere fluid-solid transition, ϕF≈0.32 and ϕM≈0.39, respectively, for d=4, and ϕF≈0.20 and ϕM≈0.25, respectively, for d=5. Although our results indicate the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension.
We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous...
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We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)].
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