ShantanuT01/DACTYL-Pretraining huggingface dataset:
At the classical level we study open bosonic strings. A generic description of string self-interactions localized at string ends is given. Self-interactions are characterized by two dimensionless coupling constants. The model is rewritten using complex Liouville fields. Using these Lorentz and reparametrization invariant variables, equations of motion get greatly simplified and reduce to some boundary problem for Liouville equation.
We present density functional theory calculations of the phonon-limited mobility in n-type monolayer graphene, silicene and MoS$_2$. The material properties, including the electron-phonon interaction, are calculated from first-principles. We provide a detailed description of the normalized full-band relaxation time approximation for the linearized Boltzmann transport equation (BTE) that includes inelastic scattering processes. The bulk electron-phonon coupling is evaluated by a supercell method. The method employed is fully numerical and does therefore not require a semi-analytic treatment of part of the problem and, importantly, it keeps the anisotropy information stored in the coupling as well as the band structure. In addition, we perform calculations of the low-field mobility and its dependence on carrier density and temperature to obtain a better understanding of transport in graphene, silicene and monolayer MoS$_2$. Unlike graphene, the carriers in silicene show strong interaction with the out-of-plane modes. We find that graphene has more than an order of magnitude higher mobility compared to silicene. For MoS$_2$, we obtain several orders of magnitude lower mobilities in agreement with other recent theoretical results. The simulations illustrate the predictive capabilities of the newly implemented BTE solver applied in simulation tools based on first-principles and localized basis sets.
We construct four new elements $3.11>m_1>m_2>m_3>m_4$ of $M\backslash L$ lying in distinct connected components of $\mathbb{R}\setminus L$, where $M$ is the Markov spectrum and $L$ is the Lagrange spectrum.   These elements are part of a decreasing sequence $(m_k)_{k\in\mathbb{N}}$ of elements in $M$ converging to $3$ and we give some evidence towards the possibility that $m_k\in M\setminus L$ for all $k\geq 1$. In particular, this indicates that $3$ might belong to the closure of $M\setminus L$, so that the answer to Bousch's question about the closedness of $M\setminus L$ might be negative.
We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply hyperellipticity, in analogy with the classical case.
Central limit theorems and asymptotic properties of the minimum-contrast estimators of the drift parameter in linear stochastic evolution equations driven by fractional Brownian motion are studied. Both singular ($H < \frac{1}{2})$ and regular ($H > \frac{1}{2})$ types of fractional Brownian motion are considered. Strong consistency is achieved by ergodicity of the stationary solution. The fundamental tool for the limit theorems and asymptotic normality (shown for Hurst parameter $H < \frac{3}{4}$) is the so-called $4^{th}$ moment theorem considered on the second Wiener chaos. This technique provides also the Berry-Esseen-type bounds for the speed of the convergence. The general results are illustrated for parabolic equations with distributed and pointwise fractional noises.
Using the semicontinuity of the Milnor number and the {\L}ojasiewicz exponent, we give a simple proof of Yau's characterization of isolated homogenous hypersurface singularities.
Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth based magnets because of the large effective spin anisotropy induced by the combination of strong spin-orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO$_3$ provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga-Luttinger liquid behavior and spinon confinement-deconfinement transitions in different regions of magnetic field-temperature phase diagram.
Bell's theorem contains the proposition that the Einstein-Podolsky-Rosen (EPR) theory (hypothesis) of the existence of elements of reality together with Einstein locality permits a mathematical description of EPR experiments by functions that are all defined on one common probability space. This proposition leads in turn to restrictions for possible experimental outcomes that Bell expressed in terms of his well known inequalities and that Vorob'ev and others had investigated before Bell. Summarizing several previous publications and adding new material, the above proposition is refuted by Einstein-local counterexamples from classical physics and shown to involve additional assumptions that can not be justified for mutually exclusive (incompatible) measurements and experiments. Moreover, criticism of our work by Mermin who invoked "standard sampling arguments" is shown to be false.
After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects whose correlation functions satisfy a discrete version of the Cauchy-Riemann relations. Their existence appears to have a deep relation with the integrability of the model, and they are presumably the lattice versions of the truly holomorphic observables appearing in the conformal field theory (CFT) describing the continuum limit. This hypothesis sheds light on the connection between CFT and integrability, and, if verified, can also be used to prove that the scaling limit of certain discrete curves in these models is described by Schramm-Loewner evolution (SLE).
We investigate two multi-shell galactic supernova remnants (SNRs), Kes79 and G352.7-0.1, to understand the causes of such morphology. The research was carried out based on new and reprocessed archival VLA observations and XMM-Newton archival data. The surrounding was investigated based on data extracted from the HI Canadian Galactic Plane Survey, the 13^CO Galactic Ring Survey and the HI Southern Galactic Plane Survey. The present study revealed that the overall morphology of both SNRs is the result of the mass-loss history of their respective progenitor stars. Kes79 would be the product of the gravitational collapse of a massive O9 star evolving near a molecular cloud and within the precursor's wind-driven bubble, while G352.7-0.1 would be the result of interactions of the SNR with an asymmetric wind from the progenitor together with projection effects. No radio point source or pulsar wind nebula was found associated with the X-ray pulsar CXOU J185238.6+004020 in Kes79. The X-ray study of G352.7-0.1, on its hand, revealed that most of the thermal X-ray radiation completely fills in the interior of the remnant and originates in heated ejecta. Characteristic parameters, like radio flux, radio spectral index, age, distance, shock velocity, initial energy and luminosity, were estimated for both SNRs.
In this short note, we show an analogue of one of Alladi's and Dawsey's formulas with respect to the Ramanujan sum $c_n(m)$ for $m\geq1$. Their formulas may be viewed as the case $m=1$ in our result.
In quantum theory of gravity, we expect the Lorentz Invariance Violation (LIV) and the modification of the dispersion relation between energy and momentum for photons. The effect of the energy-dependent velocity due to the modified dispersion relation for photons was studied in the standard cosmological context by using a sample of Gamma Ray Bursts (GRBs). In this paper we mainly discuss the possible LIV effect by using different cosmological models for the accelerating universe. Due to the degeneracies among model parameters, the GRBs' time delay data are combined with the cosmic microwave background data from the Planck first year release, the baryon acoustic oscillation data at six different redshifts, as well as Union2 type Ia supernovae data, to constrain both the model parameters and the LIV effect. We find no evidence of LIV.
We discuss the implementation, to the case of compact manifolds, of the perturbative method of Friedrich-Butscher for the construction of solutions to the vaccum Einstein constraint equations. This method is of a perturbative nature and exploits the properties of the extended constraint equations ---a larger system of equations whose solutions imply a solution to the Einstein constraints. The method is applied to the construction of nonlinear perturbations of constant mean curvature initial data of constant negative sectional curvature. We prove the existence of a neighbourhood of solutions to the constraint equations around such initial data, with particular components of the extrinsic curvature and electric/magnetic parts of the spacetime Weyl curvature prescribed as free data. The space of such free data is parametrised explicitly.
Motivated by the energy dependent metric in gravity's rainbow, we will propose a new kind of energy dependent noncommutative geometry. It will be demonstrated that like gravity's rainbow, this new noncommutative geometry is described by an energy dependent metric. We will analyse the effect of this noncommutative deformation on the Schwarzschild black holes and Kerr black holes. We will perform our analysis by relating the commutative and this new energy dependent noncommutative metrics using an energy dependent Moyal star product. We will also analyze the thermodynamics of these new noncommutative black hole solutions. We will explicitly derive expression for the corrected entropy and temperature for these black hole solutions. It will be demonstrated that for these deformed solutions black remnants cannot form. This is because these correction increase rather than reduce the temperature of the black holes.
Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ fixed point.   The key is that one-dimensional Baik-Ben Arous-Peche statistics characterize the KPZ fixed point. This yields a general and elementary method that shows convergence based on previously established limit theorems.   Independently, at the same time and place Quastel and Sharkar gave an unrelated proof of KPZ convergence. The methods invite extensions in different directions: ours to polymer models, and theirs to interacting particle systems.
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with equilateral triangles defined by a finite number of triangles, called cells. A subdivision of a triangular grid graph is replacing some of its cells by plane copies of the complete graph $K_4$.   Inspired by a recent elegant result of Akrobotu et al., who classified word-representable triangulations of grid graphs related to convex polyominoes, we characterize word-representable subdivisions of triangular grid graphs. A key role in the characterization is played by smart orientations introduced by us in this paper. As a corollary to our main result, we obtain that any subdivision of boundary triangles in the Sierpi\'{n}ski gasket graph is word-representable.
We investigate the space-time regularity of the local time associated to Volterra-L\'evy processes, including Volterra processes driven by $\alpha$-stable processes for $\alpha\in(0,2]$. We show that the spatial regularity of the local time for Volterra-L\'evy process is $P$-a.s. inverse proportionally to the singularity of the associated Volterra kernel. We apply our results to the investigation of path-wise regularizing effects obtained by perturba\Ption of ODEs by a Volterra-L\'evy process which has sufficiently regular local time. Following along the lines of [15], we show existence, uniqueness and differentiablility of the flow associated to such equations.
Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. A complex analytic germ is said Lipschitz normally embedded (LNE) if its outer and inner metrics are bilipschitz equivalent. LNE seems to be fairly rare among surface singularities; the only known LNE surface germs outside the trivial case (straight cones) are the minimal singularities. In this paper, we show that a superisolated hypersurface singularity is LNE if and only if its projectivized tangent cone has only ordinary singularities. This provides an infinite family of LNE singularities which is radically different from the class of minimal singularities.
In this proceeding, we present the results of a semi-analytic study of CDM substructure as a function of the primordial power spectrum. We apply our method to several tilted models in the LCDM framework with n=0.85-1.1, sigma_8=0.65-1.2 when COBE normalized. We also study a more extreme, warm dark matter-like spectrum that is sharply truncated below a scale of 10^10 h^-1 Msun. We show that the mass fraction of halo substructure is not a strong function of spectral slope, so it likely will be difficult to constrain tilt using flux ratios of gravitationally lensed quasars. On the positive side, all of our CDM-type models yield projected mass fractions in good agreement with strong lensing estimates: f \sim 1.5% at M \sim 10^8 Msun. The truncated model produces a significantly smaller fraction, f \lsim 0.3%, suggesting that warm dark matter-like spectra may be distinguished from CDM spectra using lensing. We also discuss the issue of dwarf satellite abundances, with emphasis on the cosmological dependence of the map between the observed central velocity dispersion of Milky Way satellites and the maximum circular velocities of their host halos. In agreement with earlier work, we find that standard LCDM over-predicts the estimated count of Milky Way satellites at fixed Vmax by an order of magnitude, but tilted models do better because subhalos are less concentrated. Interestingly, under the assumption that dwarfs have isotropic velocity dispersion tensors, models with significantly tilted spectra (n \lsim 0.85, sigma_8 \lsim 0.7) may under-predict the number of large Milky Way satellites with Vmax \gsim 40 km/s.
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the divisors of $n$. Erd\H{o}s and Kac asked whether, for every $k$, the number $\alpha_k = \sum_{n\geq 1} \frac{\sigma_k(n)}{n!}$ is irrational. It is known unconditionally that $\alpha_k$ is irrational if $k\leq 3$. We prove $\alpha_4$ is irrational.
Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.
Here, we report the photoconducting response of field-effect transistors based on three atomic layers of chemical vapor transport grown WSe$_2$ crystals mechanically exfoliated onto SiO$_2$. We find that tri-layered WSe$_2$ field-effect transistors, built with the simplest possible architecture, can display high hole mobilities ranging from 350 cm$^2$/Vs at room temperature (saturating at a value of ~500 cm$^2$/Vs below 50 K) displaying a strong photocurrent response which leads to exceptionally high photo responsivities up to 7 A/W under white light illumination of the entire channel for power densities p < 10$^2$ W/m$^2$. Under a fixed wavelength of $\lambda$ = 532 nm and a laser spot size smaller than the conducting channel area we extract photo responsitivities approaching 100 mA/W with concomitantly high external quantum efficiencies up to ~ 40 % at room temperature. These values surpass values recently reported from more complex architectures, such as graphene and transition metal dichalcogenides based heterostructures. Also, tri-layered WSe$_2$ photo-transistors display photo response times in the order of 10 microseconds. Our results indicate that the addition of a few atomic layers considerably decreases the photo response times, probably by minimizing the interaction with the substrates, while maintaining a very high photo-responsivity.
In this paper, we study a vector conservation law that models the growth and selection of ovarian follicles. During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. This work is motivated by a multiscale mathematical model starting on the cellular scale, where ovulation or atresia result from a hormonally controlled selection process. A two-dimensional conservation law describes the age and maturity structuration of the follicular cell populations. The densities intersect through a coupled hyperbolic system between different follicles and cell phases, which results in a vector conservation law and coupling boundary conditions. The maturity velocity functions possess both a local and nonlocal character. We prove the existence and uniqueness of the weak solution to the Cauchy problem with bounded initial and boundary data.
We analyze the scattering of a planar monochromatic electromagnetic wave incident upon a Schwarzschild black hole. We obtain accurate numerical results from the partial wave method for the electromagnetic scattering cross section, and show that they are in excellent agreement with analytical approximations. The scattering of electromagnetic waves is compared with the scattering of scalar, spinor and gravitational waves. We present a unified picture of the scattering of all massless fields for the first time.
We compute the joint distribution of the site and the time at which a $d$-dimensional standard Brownian motion $B_t$ hits the surface of the ball $ U(a) =\{|{\bf x}|<a\}$ for the first time. The asymptotic form of its density is obtained when either the hitting time or the starting site $B_0$ becomes large. Our results entail that if Brownian motion is started at ${\bf x}$ and conditioned to hit $U(a)$ at time $t$ for the first time, the distribution of the hitting site approaches the uniform distribution or the point mass at $a{\bf x}/|{\bf x}|$ according as $|{\bf x}|/t$ tends to zero or infinity; in each case we provide a precise asymptotic estimate of the density. In the case when $|{\bf x}|/t$ tends to a positive constant we show the convergence of the density and derive an analytic expression of the limit density.
The discovery of cosmic microwave background (CMB) was a paradigm shift in the study and fundamental understanding of the early universe and also the Big Bang phenomenon. Cosmic microwave background is one of the richest and intriguing sources of information available to cosmologists and one parameter of special interest is baryon density of the universe. Baryon density can be primarily estimated by analyzing CMB data or through the study of big bang nucleosynthesis(BBN). Hence, it is necessary that both of the results found though the two methods are in agreement with each other. Although there are some well established statistical methods for the analysis of CMB to estimate baryon density, here we explore the use of deep learning in this respect. We correlate the baryon density obtained from the power spectrum of simulated CMB temperature maps with the corresponding map image and form the dataset for training the neural network model. We analyze the accuracy with which the model is able to predict the results from a relatively abstract dataset considering the fact that CMB is a Gaussian random field. CMB is anisotropic due to temperature fluctuations at small scales but on a larger scale CMB is considered isotropic, here we analyze the isotropy of CMB by training the model with CMB maps centered at different galactic coordinates and compare the predictions of neural network models.
A classification of (super) $W$ algebras arising from non Abelian Toda and super Toda theories is presented. This classification is based on the $Sl(2)$ or $OSp(1|2)$ sub(super)algebras of the simple Lie (super)algebra underlying the model. This allows to compute the conformal spin content of each $W$ (super)algebra. {\em Based on two lectures given by L. Frappat and E. Ragoucy at the\\ XIX International Colloquium on Group Theoretical Methods in Physics\\ Salamanca (Spain), June 29 - July 4, 1992}
We study direct and indirect magnetoexcitons in Rydberg states in monolayers and heterostructures of transition-metal dichalcogenices (TMDCs) in an external magnetic field, applied perpendicular to the monolayer or heterostructures. We calculate binding energies of magnetoexcitons for the Rydberg states 1$s$, 2$s$, 3$s$, and 4$s$ by numerical integration of the Schr\"{o}dinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect magnetoexcitons. Latter allows understanding the role of screening in TMDCs heterostructures. We report the magnetic field energy contribution to the binding energies and diamagnetic coefficients (DMCs) for direct and indirect magnetoexcitons. The tunability of the energy contribution of direct and indirect magnetoexcitons by the magnetic field is demonstrated. It is shown that binding energies and DMCs of indirect magnetoexcitons can be manipulated by the number of hBN layers. Therefore, our study raises the possibility of controlling the binding energies of direct and indirect magnetostrictions in TMDC monolayers, bilayers and heterostructures using magnetic field and opens an additional degree of freedom to tailor the binding energies and DMCs for heterostructures by varying the number of hBN sheets between TMDC layers. The calculations of the binding energies and DMCs of indirect magnetoexcitons in TMDC heterostructures are novel and can be compared with the experimental results when they will be available.
At the low temperatures achieved in cool brown dwarf and hot giant planet atmospheres, the less refractory neutral alkali metals assume an uncharacteristically prominent role in spectrum formation. In particular, the wings of the Na-D (5890 \AA) and K I (7700 \AA) resonance lines come to define the continuum and dominate the spectrum of T dwarfs from 0.4 to 1.0 \mic. Whereas in standard stellar atmospheres the strengths and shapes of the wings of atomic spectral lines are rarely needed beyond 25 \AA of a line center, in brown dwarfs the far wings of the Na and K resonance lines out to 1000's of \AA detunings are important. Using standard quantum chemical codes and the Unified Franck-Condon model for line profiles in the quasi-static limit, we calculate the interaction potentials and the wing line shapes for the dominant Na and K resonance lines in H$_2$- and helium-rich atmospheres. Our theory has natural absorption profile cutoffs, has no free parameters, and is readily adapted to spectral synthesis calculations for stars, brown dwarfs, and planets with effective temperatures below 2000 Kelvin.