ShantanuT01/DACTYL-Pretraining huggingface dataset:
Fast proton conduction mechanism is of key importance for achieving high performance in fuel cell membranes, batteries, supercapacitors, and electrochromic materials. Enhanced proton diffusion is often observed in hydrated materials where it is thought to occur via the famous Grotthuss mechanism through pathways formed by structural water. Using first-principles density-functional theory calculations, we demonstrate that proton diffusion in tungsten oxide dihydrate (WO$_{3}$.2H$_{2}$O), a known good proton conductor, takes place within the layers of corner-sharing WO$_{6}$ octahedra without direct involvement of structural water. The calculated proton migration barrier in WO$_{3}$.2H$_{2}$O (0.42 eV) is in good agreement with the experimental value inferred from the temperature dependence of conductivity (0.36 eV). The preferred proton diffusion path in WO$_{3}$.2H$_{2}$O is essentially the same as in $\gamma$-WO$_{3}$, and we find an activation energy of 0.35 eV for the latter, which agrees well with the experimental values. In contrast to the small intercalation voltages calculated for WO$_{3}$ and WO$_{3}$.2H$_{2}$O, we find that proton absorption in the monohydrate WO$_{3}$.H$_{2}$O is energetically highly favorable, corresponding to voltages in excess of 1 eV in the dilute limit. However, strong proton-proton repulsion limits the equilibrium H content at zero voltage. We find a fast one-dimensional diffusion channel in WO$_{3}$.H$_{2}$O with an activation energy of only 0.07 eV at dilute proton concentrations, but much higher barriers are expected at near-equilibrium concentrations due to strong repulsive interactions with other protons. Our results illustrate that low proton diffusion barriers and low insertion voltages both contribute to fast proton transport in bulk WO$_{3}$.2H$_{2}$O and $\gamma$-WO$_{3}$.
I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order and cross over types are examined. A conformal mapping is introduced, which may be used to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$ starting from lattice QCD results at $\mu^{2}\leq 0$. This method allows us to improve the convergence of a Taylor expansion about $\mu=0$ and to enhance the sensitivity to physical singularities in the complex $\mu$ plane. The technique is illustrated by an application to a second-order transition in a chiral effective model.
The current paper presents the third part of the study devoted to composites formed by fullerene C60 and two graphene nanosheets ([C60+(5,5)] and ([C60+(9, 8)] graphene nanobuds). The formation of composites is considered from the basic points related to the atomic chemical reactivity of the fullerene molecule and nanographene. The barrier that governs the composites formation is determined in terms of the coupling energy and is expanded over two contributions that present the total energy of deformation of the composites' components and the energy of covalent coupling. In view of these energetic parameters and in contrast to expectations, seemingly identical reactions that are responsible for the formation of intermolecular contacts in (C60)2 dimer, [C60+(4,4)] carbon nanobuds, and [C60+(5,5)] and [C60+(9,8)] graphene nanobuds result in different final products. The peculiarity is suggested to result from a topochemical character of the covalent coupling between two members of the sp2 nanocarbons' family. The computations were performed by using the AM1 semiempirical version of unrestricted broken symmetry Hartree-Fock approach.
In this paper, we address the following two general problems: given two algebraic varieties in ${\bf C}^n$, find out whether or not they are (1) isomorphic; (2) equivalent under an automorphism of ${\bf C}^n$. Although a complete solution of either of these problems is out of the question at this time, we give here some handy and useful invariants of isomorphic as well as of equivalent varieties. Furthermore, and more importantly, we give a universal procedure for obtaining all possible algebraic varieties isomorphic to a given one, and use it to construct numerous examples of isomorphic, but inequivalent algebraic varieties in ${\bf C}^n$.   Among other things, we establish the following interesting fact: for isomorphic hypersurfaces $\{p(x_1,...,x_n)=0\}$ and $\{q(x_1,...,x_n)=0\}$, the number of zeros of $grad(p)$ might be different from that of $grad(q)$.
Here we prove an isoperimetric inequality for the harmonic mean of the first $N-1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of $\mathbb{S}^N$.
Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states -- the G-injective Projected Entangled Pair States (PEPS) -- on a quantum computer. Important examples include the resonant valence bond (RVB) states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors, and inverse-polynomially in the spectral gap of the PEPS parent Hamiltonian.
Motivated by studies in accelerator physics this paper computes the asymptotic behavior of the series $\displaystyle \sum_{k=1}^N \varphi(k) I_N\left(\frac{1}{k}\right)$, where $\varphi(k)$ is Euler's Totient function and $\displaystyle I_N\left(\frac{1}{k}\right)$ is the position that $1/k$ occupies in the Farey sequence of order $N$. To this end an exact formula for $\displaystyle I_N\left(\frac{1}{k}\right)$ is derived when all integers in $\displaystyle \left[2,\left\lceil \frac{N}{k} \right\rceil\right]$ are divisors of $N$.
For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $\theta$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for $S_0$ are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
We discuss the Isgur-Wise function $\xi (y)$ in the small velocity (SV) limit within the QCD sum rule method. The behavior of $\xi (y)$ in the SV limit is sensitive to the particular form of the duality relations used to decontaminate the sum rule predictions from the continuum contribution. Peculiarities of the duality relations in the problem at hand are revealed. It is shown that the proper requirements of duality and angular isotropy for S wave states lead to an unambiguous form of the sum rules for the Isgur-Wise function. We illustrate the constraints due to these requirements using a toy model of the harmonic oscillator. The slope parameter and the shape of $\xi (y)$ are determined.
We present the exact solutions to the equations of the lowest energy states of the colored and color-symmetric sectors of the Bonn quark model, which is SU(3) symmetric and is defined in terms of an effective pairing force with $su(4)$ algebraic structure. We show that the groundstate of the model is not color symmetrical except for a narrow interval in the range of possible quark numbers. We also study the performance of the Glauber coherent state, as well as of superconducting states of the BCS type, with respect to the description, not only of the absolute (colored) groundstate, but also of the minimum energy state of the color-symmetrical sector, finding that it is remarkably good. We use the model to discuss, in a schematic context, some controversial aspects of the conventional treatment of color superconductivity.
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.
We study the behaviour of the contact process with rapid stirring on the lattice $\Z^d$ in dimensions $d\geq 3$. This process was studied earlier by Konno and Katori, who proved results for the speed of convergence of the critical value as the rate of stirring approaches infinity. %Katori has improved the result of Katori in $d\geq 3$ and has produced an interval where the critical value must lie.   In this article we improve the results of Konno and Kattori and establish the sharp asymptotics of the critical value in dimensions $d\geq 3$.
If X is a complex projective variety with klt singularities, then the mixed Hodge structures on the first two singular cohomology groups are pure. We describe the pieces of the Hodge decomposition in terms of reflexive differential forms. Applications include a Lefschetz (1,1) Theorem and a weak analogue of the Hodge-Riemann bilinear relations for klt varieties.
We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the $z$ component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the $xy$ plane. We find that linearly polarized driving fields induce a second-harmonic response, while circularly polarized fields generate only a zero-frequency response, leading to a magnetization with a direction determined by the helicity. Employing an unbiased numerical method, we demonstrate the nonlinear magnetic effect driven by the circularly polarized field in the XXZ model and show that the magnitude of the magnetization can be predicted by the dynamical spin structure factor in the linear response regime.
For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.
The induced gravitational collapse (IGC) paradigm has been successfully applied to the explanation of the concomitance of gamma-ray bursts (GRBs) with supernovae (SNe) Ic. The progenitor is a tight binary system composed by a carbon-oxygen (CO) core and a neutron star (NS) companion. The explosion of the SN leads to hypercritical accretion onto the NS companion which reaches the critical mass, hence inducing its gravitational collapse to a black hole (BH) with consequent emission of the GRB. The first estimates of this process were based on a simplified model of the binary parameters and the Bondi-Hoyle-Lyttleton accretion rate. We present here the first full numerical simulations of the IGC phenomenon. We simulate the core-collapse and SN explosion of CO stars to obtain the density and ejection velocity of the SN ejecta. We follow the hydrodynamic evolution of the accreting material falling into the Bondi-Hoyle surface of the NS all the way up to its incorporation to the NS surface. The simulations go up to BH formation when the NS reaches the critical mass. For appropriate binary parameters the IGC occurs in short timescales (100-1000s) owing to the combined effective action of the photon trapping and the neutrino cooling near the NS surface. We also show that the IGC scenario leads to a natural explanation for why GRBs are associated only to SN Ic with totally absent or very little helium.
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes its values in a separable Hilbert space and the control domain need not be convex. The result is obtained by using the adjoint backward stochastic differential equation.
Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced breakage at the nano-scale for one-dimensional systems. We test it on a simple approximation and find that the probability of breakage controls distinct regimes, characterized by sharp crossovers and narrow peaks in the thermal fluctuations and specific heat. Our work provides predictions on clustering of new phases, of relevance in nano-fabrication.
We present a comparative seismic study of conditions around and beneath isolated sunspots. Using the European Grid of Solar Observations' Solar Feature Catalogue of sunspots derived from SOHO/MDI continuum and magnetogram data, 1996-2005, we identify a set of isolated sunspots by checking that within a Carrington Rotation there were no other spots detected in the vicinity. We then use level-2 tracked MDI Dopplergrams available from SOHO website to investigate wave-speed perturbations of such sunspots using time-distance helioseismology.
We apply the shell-model wave-functions of $^{76}Ge$ to calculate the nuclear matrix elements and the half-life of the $2\nu\beta\beta$ decay in $^{76}Ge$. Our result is comparable to the recent observed $2\nu\beta\beta$-decay half-life of $^{76}Ge$. Furthemore it provides the upper limit of the effective neutrino mass is about 0.4 eV from the recent experimental data of the $0\nu\beta\beta$-decay half-life.
We extend a formula of Duke, Imam\=oglu, and T\'oth (which itself is a generalization of the Katok-Sarnak formula) to prove the Kohnen-Zagier formula for Maass forms for $\Gamma_0(4)$.
We investigate the dynamics of a flat isotropic brane Universe with two-component matter source: perfect fluid with the equation of state $p=(\gamma-1) \rho$ and a scalar field with a power-law potential $V \sim \phi^{\alpha}$. The index $\alpha$ can be either positive or negative. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor (so called scaling solutions). In the nonstandard brane regime when the brane is driven by energy density square term these solutions are rather different from their analogs in the standard cosmology. A particular attention is paid to the inverse square potential. Its dynamical properties in the nonstandard brane regime are in some sense analogous to those of the exponential potential in the standard cosmology. Stability analysis of the scaling solutions are provided. We also describe solutions existing in regions of the parameter space where the scaling solutions are unstable or do not exist.
In this paper are summarized the main advances of the last years in the field of SN spectra . The arguments against a monodimensional sequence for SNIa are discussed as well as the efforts to improve the temporal and spectral coverage of this kind of SNe, with the aim to understand the physics of the explosions for their use as cosmological distance indicators. Although variety is the main character of core-collapse SNe, we have been recently surprised by both exceptionally under- and over-energetic explosions. The main properties of these two extreme subclasses are here reviewed.
Correlated magnetic noise in the form of Schumann resonances could introduce limitations to the gravitational-wave background searches of future Earth-based gravitational-wave detectors. We consider recorded magnetic activity at a candidate site for the Einstein Telescope, and forecast the necessary measures to ensure that magnetic contamination will not pose a threat to the science goals of this third-generation detector. In addition to global magnetic effects, we study local magnetic noise and the impact it might have on co-located interferometers. We express our results as upper limits on the coupling function of magnetic fields to the interferometer arms, implying that any larger values of magnetic coupling into the strain channel would lead to a reduction in the detectors' sensitivity. For gravitational-wave background searches below $\sim 30$ Hz it will be necessary for the Einstein Telescope magnetic isolation coupling to be two to four orders of magnitude better than that measured in the current Advanced LIGO and Virgo detectors.
Given a spectrally negative L\'evy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever it is above it. We also consider the versions with additional classical reflection above and/or below. Using scale functions and excursion theory, various fluctuation identities are computed in terms of the scale function. Applications in de Finetti's dividend problems are also discussed.
We present the results of 16 years of monitoring stellar orbits around the massive black hole in center of the Milky Way using high resolution NIR techniques. This work refines our previous analysis mainly by greatly improving the definition of the coordinate system, which reaches a long-term astrometric accuracy of 300 microarcsecond, and by investigating in detail the individual systematic error contributions. The combination of a long time baseline and the excellent astrometric accuracy of adaptive optics data allow us to determine orbits of 28 stars, including the star S2, which has completed a full revolution since our monitoring began. Our main results are: all stellar orbits are fit extremely well by a single point mass potential to within the astrometric uncertainties, which are now 6 times better than in previous studies. The central object mass is (4.31 +- 0.06|stat +- 0.36|R0) * 10^6 M_sun where the fractional statistical error of 1.5 percent is nearly independent from R0 and the main uncertainty is due to the uncertainty in R0. Our current best estimate for the distance to the Galactic Center is R0 = 8.33 +- 0.35 kpc. The dominant errors in this value is systematic. The mass scales with distance as (3.95 +- 0.06) * 10^6 M_sun * (R0/8kpc)^2.19. The orientations of orbital angular momenta for stars in the central arcsecond are random. We identify six of the stars with orbital solutions as late type stars, and six early-type stars as members of the clockwise rotating disk system, as was previously proposed. We constrain the extended dark mass enclosed between the pericenter and apocenter of S2 at less than 0.066, at the 99% confidence level, of the mass of Sgr A*. This is two orders of magnitudes larger than what one would expect from other theoretical and observational estimates.
Poly (triazine imide) (PTI) is a material belonging to the group of carbon nitrides and has shown to have competitive properties compared to melon or g-C3N4, especially in photocatalysis. As most of the carbon nitrides PTI is usually synthesized by thermal or hydrothermal approaches. We present and discuss an alternative synthesis for PTI which exhibits a pH dependent solubility in aqueous solutions. This synthesis is based on the formation of radicals during electrolysis of an aqueous melamine solution, coupling of resulting melamine radicals and the final formation of PTI. We applied different characterization techniques to identify PTI as the product of this reaction and report the first liquid state NMR experiments on a triazine-based carbon nitride. We show that PTI has a relatively high specific surface area and a pH dependent adsorption of charged molecules. This tunable adsorption has a significant influence on the photocatalytic properties of PTI which we investigated in dye degradation experiments.
In the simple case of a constant equation of state, redshift distribution of collapsed structures may constrain dark energy models. Different dark energy models having the same energy density today but different equations of state give quite different number counts. Moreover, we show that introducing the possibility that dark energy collapses with dark matter (``inhomogeneous'' dark energy) significantly complicates the picture. We illustrate our results by comparing four dark energy models to the standard $\Lambda$-model. We investigate a model with a constant equation of state equal to -0.8, a phantom energy model and two scalar potentials (built out of a combination of two exponential terms). Although their equations of state at present are almost indistinguishable from a $\Lambda$-model, both scalar potentials undergo quite different evolutions at higher redshifts and give different number counts. We show that phantom dark energy induces opposite departures from the $\Lambda$-model as compared with the other models considered here. Finally, we find that inhomogeneous dark energy enhances departures from the $\Lambda$-model with maximum deviations of about 15% for both number counts and integrated number counts. Larger departures from the $\Lambda$-model are obtained for massive structures which are rare objects making it difficult to statistically distinguish between models.
We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.
We present a model for neutrino oscillations in the presence of a deconstructed non-gravitational large extra dimension compactified on the boundary of a two-dimensional disk. In the deconstructed phase, sub-mm lattice spacings are generated from the hierarchy of energy scales between 1 TeV and the usual B-L breaking scale 10^{15} GeV. Here, short distance cutoffs down to 1 eV can be motivated by the strong coupling behavior of gravity in local discrete extra dimensions. This could make it possible to probe the discretization of extra dimensions and non-trivial field configurations in theory spaces which have only a few sites, i.e., for coarse latticizations. Thus, the model has relevance to present and future precision neutrino oscillation experiments.