ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is well known that under plastic deformation, dislocations are not only created but also move through the crystal, and their mobility is impeded by their interaction with the crystal structure. At high stress and temperature, this `drag' is dominated by phonon wind, i.e. phonons scattering off dislocations. Employing the semi-isotropic approach discussed in detail in Ref. [arXiv:1804.01586], we discuss here the approximate functional dependence of dislocation drag $B$ on dislocation velocity in various regimes between a few percent of transverse sound speed $c_t$ and $c_t$ (where $c_t$ is the effective average transverse sound speed of the polycrystal). In doing so, we find an effective functional form for dislocation drag $B(v)$ for different slip systems and dislocation characters at fixed (room) temperature and low pressure.
We consider the initial value problem for the L^2-critical defocusing Hartree equation in R^n, n \ge 3. We show that the problem is globally well posed in H^s(R^n) when 1>s> \frac{2(n-2)}{3n-4}$. We use the "I-method" combined with a local in time Morawetz estimate for the smoothed out solution.
Transition Voltage Spectroscopy (TVS) has been proposed as a tool to analyze charge transport through molecular junctions. We extend TVS to Au-vacuum-Au junctions and study the distance dependence of the transition voltage V_t(d) for clean electrodes in cryogenic vacuum. On the one hand, this allows us to provide an important reference for V_t(d)-measurements on molecular junctions. On the other hand, we show that TVS forms a simple and powerful test for vacuum tunneling models.
We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the time-dependent Tsallis entropy and generalized Fisher information have been obtained with the use of the $q$-moment approach to the Fokker-Planck equation developed in a previous study [H. Hasegawa, Phys. Rev. E {\bf 77}, 031133 (2008)]. Model calculations of the information entropies in response to an applied pulse and sinusoidal inputs have been presented.
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the blowup rate of the gradient of the underlying field. In this paper, we derive optimal gradient estimates for the wave filed of the 3-D Helmholtz system in the quasi-static regime. There are two salient features of our results that are new to the literature. First, we cover all the possible scenarios that the size of the inclusions are in different scales in terms of the asymptotic distance parameter $\epsilon$, which can be used to characterise the curvature effects of the shape of the inclusions on the field concentration. Second, our estimates can not only recover the known results in the literature for the static case, but can also reveal the interesting frequency effect on the field concentration. In fact, a novel phenomena is shown that even if the static part vanishes, field blowup can still occur due to the (low) frequency effect.
Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the central streams for an arbitrary Newton polygon in the unpolarized case. Hopefully this classification would help us to know the boundaries of other leaves and more detailed structure of the boundaries of central streams.
This paper presents a co-clustering technique that, given a collection of images and their hierarchies, clusters nodes from these hierarchies to obtain a coherent multiresolution representation of the image collection. We formalize the co-clustering as a Quadratic Semi-Assignment Problem and solve it with a linear programming relaxation approach that makes effective use of information from hierarchies. Initially, we address the problem of generating an optimal, coherent partition per image and, afterwards, we extend this method to a multiresolution framework. Finally, we particularize this framework to an iterative multiresolution video segmentation algorithm in sequences with small variations. We evaluate the algorithm on the Video Occlusion/Object Boundary Detection Dataset, showing that it produces state-of-the-art results in these scenarios.
This is a closed form evaluation of one interesting alternating series whose value is a combination of three mathematical constants, Pi, log 2, and Zeta (3).
Using a local thermometry technique, we have been able to quantitatively measure the thermal resistance $R^T$ of diffusive Andreev interferometers. We find that $R^T$ is strongly enhanced from its normal state value at low temperatures, and behaves non-linearly as a function of the thermal current through the sample. We also find that the $R^T$ oscillates as a function of magnetic flux with a fundamental period corresponding to one flux quantum $\Phi_0=h/2e$, demonstrating the phase coherent nature of thermal transport in these devices. The magnitude of $R^T$ is larger than predicted by recent numerical simulations.
The effect of antiferromagnetic interchain coupling in alternating spin (1,1/2) chains is studied by mean of a spin wave theory and density matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two dimensional (2D) generalization. Results of the ground state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling $J_{\perp}$. For the 2D case the spin wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any $J_{\perp}>0$ drives the system to a gapped ground state. Furthermore the behaviour of the correlation functions closely resemble the uniform spin-1/2 ladder. For $J_{\perp}$ lower than 0.3, however, the gap behaves quadratically as $\Delta\sim0.6 J^2_{\perp}$. Finally, it is argued that the behaviour of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.
In this paper, we investigate if it occurs a phase transition for a system of classical dimers adsorbed on a 3-4 lattice in the thermodynamic limit. We define four types of bonds (denoted by the dimers activities adsorbed in her, $x$, $y$, $u$ and $v$) and evaluated the partition function from the combinatorial method of the pfaffian and using periodic boundary conditions. We write the density of free energy per particle and the condition to his analyticity, showing that there is a critical point for a determined choice of the activities. We also numerically evaluated the integral on free energy and their derivates (entropy and specific heat) for the same case and compute the entropy density and molecular freedom per particle at high temperatures for this choice of the activities.
We have computed the evolving ultraviolet-millimeter spectral energy distribution (SED) produced by proto-galactic starbursts at high redshift, incorporating the chemical evolution of the interstellar medium in a consistent manner. Dust extinction is calculated in a novel way, that is not based on empirical calibrations of extinction curves, but rather on the lifetime of molecular clouds which delays the emergence of each successive generation of stars at ultraviolet wavelengths by typically 15 Myr. The predicted rest-frame far-infrared to millimeter-wave emission includes the calculation of molecular emission-line luminosities ($^{12}$CO and O$_{2}$ among other molecules) consistent with the evolving chemical abundances. Here we present details of this new model, along with the results of comparing its predictions with several high-redshift observables, namely: the ultraviolet SEDs of Lyman-limit galaxies, the high-redshift radiogalaxies 4C41.17 and 8C1435, the SCUBA sub-millimeter survey of the Hubble Deep Field (HDF), and the SEDs of intermediate-redshift elliptical galaxies. With our new reddening method, we are able to fit the spectrum of the Lyman-limit galaxy 1512-cB58, and we find an extinction of about 1.9 magnitudes at 1600 {\AA}. The model also predicts that most Lyman-limit galaxies should have a value of $\alpha$ inside that range, as it is observed. The 850 $\mu$m flux density of a typical Lyman-limit galaxy is expected to be only $\simeq 0.5$ mJy, and therefore the optical counterparts of the most luminous sub-mm sources in the HDF (or any other currently feasible sub-mm survey) are unlikely to be Lyman-break galaxies.
We consider the wave equation with a cubic convolution $\partial_t^2 u-\Delta u=(|x|^{-\gamma}*u^2)u$ in three space dimensions. Here, $0<\gamma<3$ and $*$ stands for the convolution in the space variables. It is well known that if initial data are smooth, small and compactly supported, then $\gamma\ge2$ assures unique global existence of solutions. On the other hand, it is also well known that solutions blow up in finite time for initial data whose decay rate is not rapid enough even when $2\le \gamma<3$. In this paper, we consider the Cauchy problem for $2\le \gamma<3$ in the space-time weighted $L^\infty$ space in which functions have critical decay rate. When $\gamma=2$, we give an optimal estimate of the lifespan. This gives an affirmative answer to the Kubo conjecture (see Remark right after Theorem 2.1 in Kubo(2004)). When $2<\gamma<3$, we also prove unique global existence of solutions for small data.
Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, a subset ${\cal F}$ of $G$ is an intersecting set if every pair of elements of ${\cal F}$ is intersecting. The intersection density $\rho(G)$ of a transitive permutation group $G$ is the maximum value of the quotient $|{\cal F}|/|G_v|$ where $G_v$ is a stabilizer of $v\in V$ and ${\cal F}$ runs over all intersecting sets in $G$. Intersection densities of transitive groups of degree $pq$, where $p>q$ are odd primes, is considered. In particular, the conjecture that the intersection density of every such group is equal to $1$ (posed in [ J.~Combin. Theory, Ser. A 180 (2021), 105390]) is disproved by constructing a family of imprimitive permutation groups of degree $pq$ (with blocks of size $q$), where $p=(q^k-1)/(q-1)$, whose intersection density is equal to $q$. The construction depends heavily on certain equidistant cyclic codes $[p,k]_q$ over the field $\mathbb{F}_q$ whose codewords have Hamming weight strictly smaller than $p$.
We present V and B-band CCD photometry of 35 RR Lyr stars in the southern hemisphere globular cluster NGC 6362. Fourier decomposition of the light curves was used to estimate the basic properties of these variables. From the analysis of the RRc stars we obtain a mean mass of M=0.531+/-0.014 $M_\odot$, luminosity log L=1.656+/-0.006, effective temperature Teff=7429+/-20, and helium abundance Y=0.292+/-0.002. The mean values of the absolute magnitude, metallicity (on Jurcsik's scale) and effective temperature for 14 RRab stars with "regular" light curves are: M_V=0.86+/-0.01, [Fe/H]=-0.93+/-0.04 and Teff=6555+/-25, respectively. From the B-V colors, periods and metallicities of the RRab stars we estimate the color excess for NGC 6362 to be equal to E(B-V)=0.08+/-0.01. Using this value we derive the colors of the blue and red edges of the instability strip in NGC 6362 to be $(B-V)^{BE}_0=0.17$ and $(B-V)^{RE}_0=0.43$. From the relations between the Fourier coefficients of RRab and RRc stars and their absolute magnitudes we estimate the apparent distance modulus to NGC 6362 to be (m-M)_V=14.46+/-0.10. From the mean value of log L of the RRc stars we obtain 14.59+/-0.03. The V-band light curves of three of the RRc stars exhibit changes in amplitude of over 0.1 mag on the time scale of around one week. Near the radial 1st overtone frequency we find one or two peaks, which strongly suggests that these variables belong to the newly identified group of non-radial pulsating RR Lyr stars.
We present a deep, low-frequency radio continuum study of the nearby Fanaroff--Riley class I (FR I) radio galaxy 3C 31 using a combination of LOw Frequency ARray (LOFAR; 30--85 and 115--178 MHz), Very Large Array (VLA; 290--420 MHz), Westerbork Synthesis Radio Telescope (WSRT; 609 MHz) and Giant Metre Radio Telescope (GMRT; 615 MHz) observations. Our new LOFAR 145-MHz map shows that 3C 31 has a largest physical size of $1.1$ Mpc in projection, which means 3C 31 now falls in the class of giant radio galaxies. We model the radio continuum intensities with advective cosmic-ray transport, evolving the cosmic-ray electron population and magnetic field strength in the tails as functions of distance to the nucleus. We find that if there is no in-situ particle acceleration in the tails, then decelerating flows are required that depend on radius $r$ as $v\propto r^{\beta}$ ($\beta\approx -1$). This then compensates for the strong adiabatic losses due to the lateral expansion of the tails. We are able to find self-consistent solutions in agreement with the entrainment model of Croston & Hardcastle, where the magnetic field provides $\approx$$1/3$ of the pressure needed for equilibrium with the surrounding intra-cluster medium (ICM). We obtain an advective time-scale of $\approx$$190$ Myr, which, if equated to the source age, would require an average expansion Mach number ${\cal M} \approx 5$ over the source lifetime. Dynamical arguments suggest that instead, either the outer tail material does not represent the oldest jet plasma or else the particle ages are underestimated due to the effects of particle acceleration on large scales.
We report on results of recent, high resolution hydrodynamic simulations of the formation and evolution of X-ray clusters of galaxies carried out within a cosmological framework. We employ the highly accurate piecewise parabolic method (PPM) on fixed and adaptive meshes which allow us to resolve the flow field in the intracluster gas. The excellent shock capturing and low numerical viscosity of PPM represent a substantial advance over previous studies using SPH. We find that in flat, hierarchical cosmological models, the ICM is in a turbulent state long after turbulence generated by the last major merger should have decayed away. Turbulent velocites are found to vary slowly with cluster radius, being $\sim 25%$ of $\sigma_{vir}$ in the core, increasing to $\sim 60%$ at the virial radius. We argue that more frequent minor mergers maintain the high level of turbulence found in the core where dynamical times are short. Turbulent pressure support is thus significant throughout the cluster, and results in a somewhat cooler cluster ($T/T_{vir} \sim .8$) for its mass. Some implications of cluster turbulence are discussed.
Starting with a very pedestrian point of view we compare two different at the first glance definitions for an algebra associated to BPS states in supersymmetric fields theories. One proposed by Harvey and Moore exploits $S$-matrices of BPS states as structure constants of a new algebra. Another one proposed by Kontsevich and Soibelman gives a construction according to the structure of cohomological Hall algebras. We show these two constructions give equivalent algebras.
In this report, a scheme different from the PT and Wootters concurrence is developed to acquire a criterion to investigate the bipartite separability of the Werner state.
We present an experimental characterization of the statistics of multiple photon pairs produced by spontaneous parametric down-conversion realized in a nonlinear medium pumped by high-energy ultrashort pulses from a regenerative amplifier. The photon number resolved measurement has been implemented with the help of a fiber loop detector. We introduce an effective theoretical description of the observed statistics based on parameters that can be assigned direct physical nterpretation. These parameters, determined for our source from the collected experimental data, characterize the usefulness of down-conversion sources in multiphoton interference schemes that underlie protocols for quantum information processing and communication.
We analyse a collection of twisted mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae comprising on some instances secondary terms of the shape $P(\log T) T^{C}$ for a suitable constant $C<1$ and a polynomial $P(x)$. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$-conjecture.
A review is provided of our current theoretical understanding of dynamic scaling in nonequilibrium interface growth as, for example, in MBE growth under ultrahigh vacuum deposition conditions.
Let $p$ be an odd prime number and let $X_0^+(p)$ be the quotient of the classical modular curve $X_0(p)$ by the action of the Atkin-Lehner operator $w_p$. In this paper we show how to compute explicit equations for the canonical model of $X_0^+(p)$. Then we show how to compute the modular parametrization, when it exists, from $X_0^+(p)$ to an isogeny factor $E$ of dimension 1 of its jacobian $J_0^+(p)$. Finally we show how use this map to determine the rational points on $X_0^+(p)$ up to a large fixed height.
The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potential, these sum rules are studied for Green's functions that are derived self-consistently within the $T$ matrix approximation at finite temperature.
If the lightest chargino is discovered at LEP2, the measurement of its mass and cross section together with the mass of the lightest neutralino, enables the determination of the parameters that define the theory and the entire supersymmetric and Higgs spectrum. Within this context, we: (i) study the effect of the one--loop tadpoles in the minimization condition of the Higgs potential, by comparing the RGE--improved Higgs potential approximation with the calculation of the minimum including the effect of the one--loop tadpoles, and (ii) compare the prediction of two different supergravity models, namely, the model based on $B=2m_0$ and motivated by the solution of the $\mu$--problem, and the minimal supergravity model, based on $A=B+m_0$.
Most coding theorems in quantum Shannon theory can be proven using the decoupling technique: to send data through a channel, one guarantees that the environment gets no information about it; Uhlmann's theorem then ensures that the receiver must be able to decode. While a wide range of problems can be solved this way, one of the most basic coding problems remains impervious to a direct application of this method: sending classical information through a quantum channel. We will show that this problem can, in fact, be solved using decoupling ideas, specifically by proving a "dequantizing" theorem, which ensures that the environment is only classically correlated with the sent data.   Our techniques naturally yield a generalization of the Holevo-Schumacher-Westmoreland Theorem to the one-shot scenario, where a quantum channel can be applied only once.
Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high-T_c cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.
New generation large-aperture telescopes, multi-object spectrographs, and large format detectors are making it possible to acquire very large samples of stellar spectra rapidly. In this context, traditional star-by-star spectroscopic analysis are no longer practical. New tools are required that are capable of extracting quickly and with reasonable accuracy important basic stellar parameters coded in the spectra. Recent analyses of Artificial Neural Networks (ANNs) applied to the classification of astronomical spectra have demonstrated the ability of this concept to derive estimates of temperature and luminosity. We have adapted the back-propagation ANN technique developed by von Hippel et al. (1994) to predict effective temperatures, gravities and overall metallicities from spectra with resolving power ~ 2000 and low signal-to-noise ratio. We show that ANN techniques are very effective in executing a three-parameter (Teff,log g,[Fe/H]) stellar classification. The preliminary results show that the technique is even capable of identifying outliers from the training sample.
The density dependent relativistic hadron field theory(DDRH) is extended to inclusions of pentaquark $\Theta^+$. We investigate In-medium properties of $\Theta^+$ and nucleons. As well as the neutron and proton,the effective $\Theta^+$ mass decreases as the baryon density increases,and remains larger than nucleons'. The effective mass of $\Theta^+$ is calculated,$M^*_{\Theta^+}\simeq0.71M_{\Theta^+}$ at normal nuclear density with the fraction of $\Theta^+$ 0.2. The effective masses of all baryon increase with the increasing fraction of $\Theta^+$. The binding energy is also studied. We find the binding energy is much larger than it in nuclear matter without $\Theta^+$,and then discuss the stability of the system with conclusions of pentaquark $\Theta^+$. It is shown that the system becomes bounder added small fraction of $\Theta^+$. Finally we discuss the condition when the system is the most stable and calculate the minimum of binding energy and the fractions of all baryons as functions of baryon density.
The trapped Bose system can be regarded as two-dimensional if the thermal fluctuation energy is less than the lowest energy in the perpendicular direction. Under this assumption, we derive an expression for the maximum thickness of an effective two-dimensional trapped Bose system.
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on observability inequalities and a special choice of initial conditions, we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.
We derive the first law of binary point-particle mechanics for generic bound (i.e. eccentric) orbits at the fourth post-Newtonian (4PN) order, accounting for the non-locality in time of the dynamics due to the occurence of a gravitational-wave tail effect at that order. Using this first law, we show how the periastron advance of the binary system can be related to the averaged redshift of one of the two bodies for a slightly non-circular orbit, in the limit where the eccentricity vanishes. Combining this expression with existing analytical self-force results for the averaged redshift, we recover the known 4PN expression for the circular-orbit periastron advance, to linear order in the mass ratio.
We show for even positive integers $n$ that the quotient of the Riemann zeta values $\zeta(n+1)$ and $\zeta(n)$ satisfies the equation $$\frac{\zeta(n+1)}{\zeta(n)} = (1-\frac{1}{n}) (1-\frac{1}{2^{n+1}-1}) \frac{\mathcal{L}^\star(\mathfrak{p}_n)}{\mathfrak{p}_n'(0)},$$ where $\mathfrak{p}_n \in \mathbb{Z}[x]$ is a certain monic polynomial of degree $n$ and $\mathcal{L}^\star: \mathbb{C}[x] \to \mathbb{C}$ is a linear functional, which is connected with a special Dirichlet series. There exists the decomposition $\mathfrak{p}_n(x) = x(x+1) \mathfrak{q}_n(x)$. If $n = p+1$ where $p$ is an odd prime, then $\mathfrak{q}_n$ is an Eisenstein polynomial and therefore irreducible over $\mathbb{Z}[x]$.