ShantanuT01/DACTYL-Pretraining huggingface dataset:
The curvature correction term to the surface tension is used as a criterion for the efficiency of the Skyrme interaction in describing surface properties. Based on the nuclear equation of state, the curvature correction term to the surface tension coefficient is calculated for 97 standard Skyrme interaction parameter sets in the vicinity of nuclear saturation density at zero temperature. The main idea is to find those parametrizations that give the Tolman's $\delta$ correction close to the available theoretical predictions from the statistical theory. Only 59 out of 97 models give satisfactory results. Comparison of the obtained results with the results of the implementation of different macroscopic and microscopic constraints to Skyrme parametrizations available in the literature allows us to select 4 models that satisfy all the constraints.
In-medium effects on transverse-mass distributions of quarks and gluons are considered assuming a possible local equilibrium for colorless quark objects (mesons and baryons) created in central A-A collisions. It is shown that the average transverse momentum squared for these partons grows and then saturates when the initial energy increases. Within the quark-gluon string model it leads to the colliding energy dependence of hadron transverse mass spectra which is similar to that observed in heavy ion collisions. Comparison with other scenarios is given.
Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field $A^D_i$ (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field $A^N_a$ (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields $A^N_a$ and $A^D_i$ are T-dual to ${}^\star A_D^a$ and ${}^\star A_N^i$ respectively.   We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable $y_\mu$ and its double ${\tilde y}_\mu$. This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.
We prove deviation bounds for the random variable $\sum_{i=1}^{n} f_i(Y_i)$ in which $\{Y_i\}_{i=1}^{\infty}$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \rightarrow [-a_i, a_i]$. Our bound improves upon previously known bounds in that the dependence is on $\sqrt{a_1^2+\cdots+a_n^2}$ rather than $\max_{i}\{a_i\}\sqrt{n}.$ We also prove deviation bounds for certain types of sums of vector--valued random variables obtained from a Markov chain in a similar manner. One application includes bounding the expected value of the Schatten $\infty$-norm of a random matrix whose entries are obtained from a Markov chain.
We define certain arithmetic derivatives on $\mathbb{Z}$ that respect the Leibniz rule, are additive for a chosen equation $a+b=c$, and satisfy a suitable non-degeneracy condition. Using Geometry of Numbers, we unconditionally show their existence with controlled size. We prove that any power-saving improvement on our size bounds would give a version of the $abc$ Conjecture. In fact, we show that the existence of sufficiently small arithmetic derivatives in our sense is equivalent to the $abc$ Conjecture. Our results give an explicit manifestation of an analogy suggested by Vojta in the eighties, relating Geometry of Numbers in arithmetic to derivatives in function fields and Nevanlinna theory. In addition, our construction formalizes the widespread intuition that the $abc$ Conjecture should be related to arithmetic derivatives of some sort.
A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a tahyonic model with the Calogero potential.
Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a 'memory term', i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn exchange-correlation (XC) kernel we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical Jellium 'gold clusters'. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the Jellium model. Two-dimensional pump-probe spectroscopy is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail. Finally, we examine memory effects on high harmonic generation, finding memory narrows emission lines.
Various facets of the concept of mass are discussed. The masses of elementary particles and the search for higgs. The masses of hadrons. The pedagogical virus of relativistic mass.
The 21cm forest -- HI absorption features in the spectra of high-redshift radio sources -- can potentially provide a unique probe of the largely neutral intergalactic medium (IGM) during the epoch of reionization. We present simulations of the 21cm forest due to the large scale structure of the reionization-era IGM, including a prescription for x-ray heating and the percolation of photoionization bubbles. We show that, if detected with future instruments such as the Square Kilometer Array (SKA), the 21cm forest can provide a significant constraint on the thermal history of the IGM. Detection will be aided by consideration of the sudden increase in signal variance at the onset of 21cm absorption. If radio foregrounds and the intrinsic source spectra are well understood, the flux decrement over wide bandwidths can also improve detection prospects. Our analysis accounts for the possibility of narrow absorption lines from intervening dense regions, but, unlike previous studies, our results do not depend on their properties. Assuming x-ray heating corresponding to a local stellar population, we estimate that a statistically significant detection of 21cm absorption could be made by SKA in less than a year of observing against a Cygnus A-type source at $z \sim 9$, as opposed to nearly a decade for a significant detection of the detailed forest features. We discuss observational challenges due to uncertainties regarding the abundance of background sources and the strength of the 21cm absorption signal.
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.
We have determined accurate values of the product of the mass-loss rate and the ion fraction of P^{4+}, Mdot q(P^{4+}), for a sample of 40 Galactic O-type stars by fitting stellar-wind profiles to observations of the P V resonance doublet obtained with FUSE, ORFEUS/BEFS, and Copernicus. When P^{4+} is the dominant ion in the wind, Mdot q(P^{4+}) approximates the mass-loss rate to within a factor of 2. Theory predicts that P^{4+} is the dominant ion in the winds of O7-O9.7 stars, though an empirical estimator suggests that the range from O4-O7 may be more appropriate. However, we find that the mass-loss rates obtained from P V wind profiles are systematically smaller than those obtained from fits to Halpha emission profiles or radio free-free emission by median factors of about 130 (if P^{4+} is dominant between O7 and O9.7) or about 20 (if P^{4+} is dominant between O4 and O7). These discordant measurements can be reconciled if the winds of O stars in the relevant temperature range are strongly clumped on small spatial scales. We use a simplified two-component model to investigate the volume filling factors of the denser regions. This clumping implies that mass-loss rates determined from "density squared" diagnostics have been systematically over-estimated by factors of 10 or more, at least for a subset of O stars. Reductions in the mass-loss rates of this size have important implications for the evolution of massive stars and quantitative estimates of the feedback that hot-star winds provide to their interstellar environments.
The impact of local space anisotropy on the transverse Doppler effect is examined. Two types of laboratory experiments aimed at seeking and measuring the local space anisotropy are proposed. In terms of the conventional special relativity theory, which treats 3D space to be locally isotropic, the experiments are of the type of ``null-experiments''. In the first-type experiments, a feasible Doppler shift of frequency is measured by the M\"ossbauer effect, with the M\"ossbauer source and absorber being located at two identical and diametrically opposed distances from the center of a rapidly rotating rotor, while the $\gamma$-quanta are recorded by two stationary and oppositely positioned proportional counters. Either of the counters records only those $\gamma$-quanta that passed through the absorber at the moment of the passage of the latter near a counter. The second-type experiments are made using the latest radio physics techniques for generating monochromatic oscillations and for recording weak signals. The effect expected due to space anisotropy consists in frequency modulation of the harmonic oscillations coming to a receiver that rotates at a constant velocity around the monochromatic wave emitter. In this case the modulation depth proves to be proportional to the space anisotropy magnitude.
Defects in semiconductors can exhibit multiple charge states, which can be used for charge storage applications. Here we consider such charge storage in a series of oxygen deficient phases of TiO$_2$, known as Magn\'eli phases. These Ti$_n$O$_{2n-1}$ Magn\'eli phases present well-defined crystalline structures, i. e., their deviation from stoichiometry is accommodated by changes in space group as opposed to point defects. We show that these phases exhibit intermediate bands with the same electronic quadruple donor transitions akin to interstitial Ti defect levels in TiO$_2$-rutile. Thus, the Magn\'eli phases behave as if they contained a very large pseudo-defect density: $\frac{1}{2}$ per formula unit Ti$_n$O$_{2n-1}$. Depending on the Fermi Energy the whole material will become charged. These crystals are natural charge storage materials with a storage capacity that rivals the best known supercapacitors.
Our goal is to estimate the star formation main sequence (SFMS) and the star formation rate density (SFRD) at z <= 0.017 (d < 75 Mpc) using the Javalambre Photometric Local Universe Survey (J-PLUS) first data release, that probes 897.4 deg2 with twelve optical bands. We extract the Halpha emission flux of 805 local galaxies from the J-PLUS filter J0660, being the continuum level estimated with the other eleven J-PLUS bands, and the dust attenuation and nitrogen contamination corrected with empirical relations. Stellar masses (M), Halpha luminosities (L), and star formation rates (SFRs) were estimated by accounting for parameters covariances. Our sample comprises 689 blue galaxies and 67 red galaxies, classified in the (u-g) vs (g-z) color-color diagram, plus 49 AGN. The SFMS is explored at log M > 8 and it is clearly defined by the blue galaxies, with the red galaxies located below them. The SFMS is described as log SFR = 0.83 log M - 8.44. We find a good agreement with previous estimations of the SFMS, especially those based on integral field spectroscopy. The Halpha luminosity function of the AGN-free sample is well described by a Schechter function with log L* = 41.34, log phi* = -2.43, and alpha = -1.25. Our measurements provide a lower characteristic luminosity than several previous studies in the literature. The derived star formation rate density at d < 75 Mpc is log rho_SFR = -2.10 +- 0.11, with red galaxies accounting for 15% of the SFRD. Our value is lower than previous estimations at similar redshift, and provides a local reference for evolutionary studies regarding the star formation history of the Universe.
We study the recurrence/transience phase transition for Markov chains on $\mathbb{R}_+$, $\mathbb{R}$, and $\mathbb{R}^2$ whose increments have heavy tails with exponent in $(1,2)$ and asymptotically zero mean. This is the infinite-variance analogue of the classical Lamperti problem. On $\mathbb{R}_+$, for example, we show that if the tail of the positive increments is about $c y^{-\alpha}$ for an exponent $\alpha \in (1,2)$ and if the drift at $x$ is about $b x^{-\gamma}$, then the critical regime has $\gamma = \alpha -1$ and recurrence/transience is determined by the sign of $b + c\pi \textrm{cosec} (\pi \alpha)$. On $\mathbb{R}$ we classify whether transience is directional or oscillatory, and extend an example of Rogozin \& Foss to a class of transient martingales which oscillate between $\pm \infty$. In addition to our recurrence/transience results, we also give sharp results on the existence/non-existence of moments of passage times.
This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion process. A stronger estimate has been proved for the corresponding discrete time model, so we take the needed estimate as a hypothesis. The process is initially in local equilibrium with a slowly varying macroscopic profile. The macroscopic initial profile is smooth in a neighborhood of the origin where the second-class particle starts off, and the forward characteristic from the origin is not a shock. Given these assumptions, the result is that the typical fluctuation of the second-class particle is not of larger order than n^{2/3}(log n)^{1/3}, where n is the ratio of the macroscopic and microscopic space scales. The conjectured correct order should be n^{2/3}. Landim et al. have proved a lower bound of order n^{5/8} for more general asymmetric exclusion processes in equilibrium. Fluctuations in the case of shocks and rarefaction fans are covered by earlier results of Ferrari-Fontes and Ferrari-Kipnis.
In a first part, we prove a Lyapunov-type criterion for the $\xi\_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on each others when they hit $0$. Our main result is that the sequence of empirical stationary distributions of the particle system converges to the minimal quasi-stationary distribution of the birth and death process.
In this study we investigate a novel approach to stochastically perturb the disease transmission coefficient, which is a key parameter in susceptible-infected-susceptible (SIS) models. Motivated by the papers [2] and [5], we perturb the disease transmission coefficient with a Gaussian white noise, formally modelled as the time derivative of a mean reverting Ornstein-Uhlenbeck process. We remark that, thanks to a suitable representation of the solution to the deterministic SIS model, this perturbation is rigorous and supported by a Wong-Zakai approximation argument that consists in smoothing the singular Gaussian white noise and then taking limit of the solution from the approximated model. We prove that the stochastic version of the classic SIS model obtained this way preserves a crucial feature of the deterministic equation: the reproduction number dictating the two possible asymptotic regimes for the infection, i.e. extinction and persistence, remains unchanged. We then identify the class of perturbing noises for which this property holds and propose simple sufficient conditions for that. All the theoretical discoveries are illustrated and discussed with the help of several numerical simulations.
Motion of massive test particles in the nonvacuum spherically symmetric radiating Vaidya spacetime is investigated, allowing for physical interaction of the particles with the radiation field in terms of which the source energy-momentum tensor is interpreted. This "Poynting-Robertson-like effect" is modeled by the usual effective term describing a Thomson-type radiation drag force. The equations of motion are studied for simple types of motion including free motion (without interaction), purely radial and purely azimuthal (circular) motion, and for the particular case of "static" equilibrium; appropriate solutions are given where possible. The results---mainly those on the possible existence of equilibrium positions---are compared with their counterparts obtained previously for a test spherically symmetric radiation field in a vacuum Schwarzschild background.
Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From a microscopic perspective, interfacial phonon transport is described by transmission and reflection coefficients, analogous to the well-known Fresnel coefficients for light. However, these coefficients have never been directly measured, and thermal transport processes at interfaces remain poorly understood despite considerable effort. Here, we report the first measurements of the Fresnel transmission coefficients for thermal phonons at a metal-semiconductor interface using ab-initio phonon transport modeling and a thermal characterization technique, time-domain thermoreflectance. Our measurements show that interfaces act as thermal phonon filters that transmit primarily low frequency phonons, leading to these phonons being the dominant energy carriers across the interface despite the larger density of states of high frequency phonons. Our work realizes the long-standing goal of directly measuring thermal phonon transmission coefficients and demonstrates a general route to study microscopic processes governing interfacial heat conduction.
Aldous [(2007) Preprint] defined a gossip process in which space is a discrete $N\times N$ torus, and the state of the process at time $t$ is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate $N^{-\alpha}$ to a site chosen at random from the torus. We will be interested in the case in which $\alpha<3$, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove three results that precisely describe the spread of information in a slightly simplified model on the real torus. The time until everyone knows the information is asymptotically $T=(2-2\alpha/3)N^{\alpha/3}\log N$. If $\rho_s$ is the fraction of the population who know the information at time $s$ and $\varepsilon$ is small then, for large $N$, the time until $\rho_s$ reaches $\varepsilon$ is $T(\varepsilon)\approx T+N^{\alpha/3}\log (3\varepsilon /M)$, where $M$ is a random variable determined by the early spread of the information. The value of $\rho_s$ at time $s=T(1/3)+tN^{\alpha/3}$ is almost a deterministic function $h(t)$ which satisfies an odd looking integro-differential equation. The last result confirms a heuristic calculation of Aldous.
Based on the Holstein double-exchange model and a highly efficient single cluster Monte Carlo approach we study the interplay of double-exchange and polaron effects in doped colossal magneto-resistance (CMR) manganites. The CMR transition is shown to be appreciably influenced by lattice polaron formation.
Strongly correlated quantum particles in lattice potentials are the building blocks for a large variety of quantum insulators, for instance Mott phases and density waves breaking the lattice symmetry. Such collective states are accessible to bosonic and fermionic systems. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing, since density order then competes with phase separation. Here we manipulate such Bose-Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice of a GaAs bilayer. At unitary lattice filling, strong inter- and intra-species interactions stabilise insulating phases when the fraction of charged excitons is around (1/3, 1/2, 2/3). We evidence that dual Bose-Fermi density waves are then realised, with species ordered in alternating stripes. Our observations highlight that dipolar excitons allow for controlled implementations of Bose-Fermi Hubbard models extended by off-site interactions.
We establish maximal local regularity results of weak solutions or local minimizers of \[ \operatorname{div} A(x, Du)=0 \quad\text{and}\quad \min_u \int_\Omega F(x,Du)\,dx, \] providing new ellipticity and continuity assumptions on $A$ or $F$ with general $(p,q)$-growth. Optimal regularity theory for the above non-autonomous problems is a long-standing issue; the classical approach by Giaquinta and Giusti involves assuming that the nonlinearity $F$ satisfies a structure condition. This means that the growth and ellipticity conditions depend on a given special function, such as $t^p$, $\varphi(t)$, $t^{p(x)}$, $t^p+a(x)t^q$, and not only $F$ but also the given function is assumed to satisfy suitable continuity conditions. Hence these regularity conditions depend on given special functions.   In this paper we study the problem without recourse to special function structure and without assuming Uhlenbeck structure. We introduce a new ellipticity condition using $A$ or $F$ only, which entails that the function is quasi-isotropic, i.e.\ it may depend on the direction, but only up to a multiplicative constant. Moreover, we formulate the continuity condition on $A$ or $F$ without specific structure and without direct restriction on the ratio $\frac qp$ of the parameters from the $(p,q)$-growth condition. We establish local $C^{1,\alpha}$-regularity for some $\alpha\in(0,1)$ and $C^{\alpha}$-regularity for any $\alpha\in(0,1)$ of weak solutions and local minimizers. Previously known, essentially optimal, regularity results are included as special cases.