Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers

We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, tilted with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time-averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first-order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, there are important and observable quantitative differences, which we discuss.

Nonclassical rotational inertia in a two-dimensional bosonic solid containing grain boundaries

We study the occurrence of nonclassical rotational inertia (NCRI) arising from superfluidity along grain boundaries in a two-dimensionalbosonic system. We make use of a standard mapping between the zero-temperature properties of this system and the statistical mechanics of interacting vortex lines in the mixed phase of a type-II superconductor. In the mapping, the liquid phase of the vortex system corresponds to the superfluid bosonic phase. We consider numerically obtained polycrystalline configurations of the vortex lines in which the microcrystals are separated by liquidlike grain-boundary regions which widen as the vortex system temperature increases. The NCRI of the corresponding zero-temperature bosonic systems can then be numerically evaluated by solving the equations of superfluid hydrodynamics in the channels near the grain boundaries. We find that the NCRI increases very abruptly as the liquid regions in the vortex system (equivalently, superfluid regions in the bosonic system) form a connected, system-spanning structure with one or more closed loops. The implications of these results for experimentally observed supersolid phenomena are discussed.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Time scales for transitions between free-energy minima of a dense hard-sphere system

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free-energy, spends in the neighborhood of this minimum before making a transition to the basin of attraction of another free-energy minimum. This time scale is found to increase as the average density is increased. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This time scale does not show any evidence of increasing with sample size

Out of equilibrium plasticity dynamics and the annealing of supersolidity in solid He-4

We present a numerical study of a continuum plasticity field coupled to a Ginzburg-Landau model for superfluidity. The results suggest that a supersolid fraction may appear as a long-lived transient during the time evolution of the plasticity field at higher temperatures where both dislocation climb and glide are allowed. Supersolidity, however, vanishes with annealing. As the temperature is decreased, dislocation climb is arrested and any residual supersolidity due to incomplete annealing remains frozen. Our results may provide a resolution of many perplexing issues concerning a variety of experiments on bulk solid He-4.

Hydrodynamics of compressible superfluids in confined geometries

We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter (v/v(s))(2) where v is the typical speed of the flow and vs is the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a Gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems.

Ising model on a random network with annealed or quenched disorder

We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of fourfold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one-dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one-dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.

Na2.44Mn1.79(SO4)(3): a new member of the alluaudite family of insertion compounds for sodium ion batteries

Sodium-ion batteries have been extensively pursued as economic alternatives to lithium-ion batteries. Investigating the polyanion chemistry, alluaudite structured Na2Fe2II(SO4)(3) has been recently discovered as a 3.8 V positive electrode material (Barpanda et al., Nature Commun., 5: 4358, 2014). Registering the highest ever Fe-III/Fe-II redox potential (vs. Na/Na+) and formidable energy density, it has opened up a new polyanion family for sodium batteries. Exploring the alluaudite family, here we report isotypical Na2+2xMn2-xII(SO4)(3) (x = 0.22) as a novel high-voltage cathode material for the first time. Following low-temperature (ca. 350 degrees C) solid-state synthesis, the structure of this new alluaudite compound has been solved adopting a monoclinic framework (s.g. C2/c) showing antiferromagnetic ordering at 3.4 K. Synergising experimental and ab initio DFT investigation, Na2+2xMn2-xII(SO4)(3) has been found to be a potential high-voltage (ca. 4.4 V) cathode material for sodium batteries.

Ionothermal Synthesis of High-Voltage Alluaudite Na2+2xFe2-x(SO4)(3) Sodium Insertion Compound: Structural, Electronic, and Magnetic Insights

Exploring future cathode materials for sodium-ion batteries, alluaudite class of Na2Fe2II(SO4)(3) has been recently unveiled as a 3.8 V positive insertion candidate (Barpanda et al. Nat. Commun. 2014, 5, 4358). It forms an Fe-based polyanionic compound delivering the highest Fe-redox potential along with excellent rate kinetics and reversibility. However, like all known SO4-based insertion materials, its synthesis is cumbersome that warrants careful processing avoiding any aqueous exposure. Here, an alternate low temperature ionothermal synthesis has been described to produce the alluaudite Na2+2xFe2-xII(SO4)(3). It marks the first demonstration of solvothermal synthesis of alluaudite Na2+2xM2-xII(SO4)(3) (M = 3d metals) family of cathodes. Unlike classical solid-state route, this solvothermal route favors sustainable synthesis of homogeneous nanostructured alluaudite products at only 300 degrees C, the lowest temperature value until date. The current work reports the synthetic aspects of pristine and modified ionothermal synthesis of Na2+2xFe2-xII(SO4)(3) having tunable size (300 nm similar to 5 mu m) and morphology. It shows antiferromagnetic ordering below 12 K. A reversible capacity in excess of 80 mAh/g was obtained with good rate kinetics and cycling stability over 50 cycles. Using a synergistic approach combining experimental and ab initio DFT analysis, the structural, magnetic, electronic, and electrochemical properties and the structural limitation to extract full capacity have been described.

Na2M2(SO4)(3) (M = Fe, Mn, Co and Ni): towards high-voltage sodium battery applications

Sodium-ion-based batteries have evolved as excellent alternatives to their lithium-ion-based counterparts due to the abundance, uniform geographical distribution and low price of Na resources. In the pursuit of sodium chemistry, recently the alluaudite framework Na2M2(SO4)(3) has been unveiled as a high-voltage sodium insertion system. In this context, the framework of density functional theory has been applied to systematically investigate the crystal structure evolution, density of states and charge transfer with sodium ions insertion, and the corresponding average redox potential, for Na2M2(SO4)(3) (M = Fe, Mn, Co and Ni). It is shown that full removal of sodium atoms from the Fe-based device is not a favorable process due to the 8% volume shrinkage. The imaginary frequencies obtained in the phonon dispersion also reflect this instability and the possible phase transition. This high volume change has not been observed in the cases of the Co- and Ni-based compounds. This is because the redox reaction assumes a different mechanism for each of the compounds investigated. For the polyanion with Fe, the removal of sodium ions induces a charge reorganization at the Fe centers. For the Mn case, the redox process induces a charge reorganization of the Mn centers with a small participation of the oxygen atoms. The Co and Ni compounds present a distinct trend with the redox reaction occurring with a strong participation of the oxygen sublattice, resulting in a very small volume change upon desodiation. Moreover, the average deintercalation potential for each of the compounds has been computed. The implications of our findings have been discussed both from the scientific perspective and in terms of technological aspects.