ShantanuT01/DACTYL-Pretraining huggingface dataset:
In \cite{arxiv,arxiv1,Kor,cras1,cras2}, we have developed a new tool called \textit{quasi solutions} which approximate in some sense the compressible Navier-Stokes equation. In particular it allows us to obtain global strong solution for the compressible Navier-Stokes equations with \textit{large} initial data on the irrotational part of the velocity (\textit{large} in the sense that the smallness assumption is subcritical in terms of scaling, it turns out that in this framework we are able to obtain a family of large initial data in the energy space in dimension N=2). In this paper we are interested in proving the result anounced in \cite{cras3} concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are $C^{\infty}$ on $(0,T)\times\R^{N}$ for any $T>0$. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular we show that for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to $\mu(\rho)=\rho^{\alpha}$ with $\alpha>1$. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density $\rho_{0}$.
Studies of cluster X-ray scaling relations have led to suggestions that non-gravitational processes, e.g., radiative cooling and/or "preheating", have significantly modified the entropy of the intracluster medium (ICM). For the first time, we test this hypothesis through a comparison of predicted thermal Sunyaev-Zeldovich (SZ) effect scaling relations with available data from the literature. One of the relations that we explore, in principle, depends solely on SZ effect observations, thus offering an X-ray independent probe of the ICM. A detailed comparison of the theoretical relations with the largest compilation of high redshift SZ effect data to date indicates that the presence of an entropy floor is favored by the data. Furthermore, the inferred level of that floor, 300 keV cm^2 or higher, is comparable to that found in studies of X-ray scaling relations of nearby massive clusters. Thus, we find no evidence for significant evolution of the entropy floor out to z = 0.7. We further demonstrate that the high quality data to be obtained from the upcoming Sunyaev-Zeldovich Array (SZA) and the (soon-to-be) upgraded Owens Valley Radio Observatory (OVRO) array will open powerful new windows into the properties of the ICM. Specifically, the new measurements will allow for accurate measurements of the ICM entropy for even the most distant galaxy clusters.
An atom laser is a hypothetical device which would produce an atomic field analogous to the electromagnetic field of a photon laser. Here I argue that for this analogy to be meaningful it is necessary to have a precise definition of a laser which applies equally to photon or atom lasers. The definition I propose is based upon the principle that the output of a laser is well-approximated by a classical wave of fixed intensity and phase. This principle yields four quantitative conditions which the output of a device must satisfy in order for that device to be considered a laser. While explaining these requirements, I analyse the similarities and differences between atom and photon lasers. I show how these conditions are satisfied first by an idealized photon laser model, and then by a more generic model which can apply to atom lasers also. Lastly, I briefly discuss the current proposals for atom lasers and whether they could be true lasers.
We monitored the Ca II H and K lines of HD 179949, a notable star in the southern hemisphere, to observe and confirm previously identified planet induced emission (PIE) as an effect of star-planet interaction. We obtained high resolution spectra (R ~ 53,000) with a signal-to-noise ratio S/N >~ 50 in the Ca II H and K cores during 10 nights of observation at the McDonald Observatory. Wide band echelle spectra were taken using the 2.7 m telescope. Detailed statistical analysis of Ca II K revealed fluctuations in the Ca II K core attributable to planet induced chromospheric emission. This result is consistent with previous studies by Shkolnik et al. (2003). Additionally, we were able to confirm the reality and temporal evolution of the phase shift of the maximum of star-planet interaction previously found. However, no identifiable fluctuations were detected in the Ca II H core. The Al I lambda 3944 A line was also monitored to gauge if the expected activity enhancements are confined to the chromospheric layer. Our observations revealed some variability, which is apparently unassociated with planet induced activity.
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states that as long as $E$ has no Complex Multiplication (CM), the map $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$ is surjective for all but finitely many $\ell$.   We say that a prime number $\ell$ is exceptional (relative to the pair $(E,K)$) if this map is not surjective. Here we give a new bound on the largest exceptional prime, as well as on the product of all exceptional primes of $E$. We show in particular that conditionally on the Generalized Riemann Hypothesis (GRH), the largest exceptional prime of an elliptic curve $E$ without CM is no larger than a constant (depending on $K$) times $\log N_E$, where $N_E$ is the absolute value of the norm of the conductor. This answers affirmatively a question of Serre.
Let $E$ be the tilting bundle on the Grassmannian $\text{Gr}(n,r)$ of $r$-dimensional quotients of $\Bbbk^n$ constructed by Kapranov. Buchweitz, Leuschke and Van den Bergh introduced a quiver $Q$ and a surjective $\Bbbk$-algebra homomorphism $\Phi\colon\Bbbk Q\rightarrow A=\text{End}(E)$, together with a recipe on how the kernel may be computed. In this paper, for the case $r=2$ we give a new, direct proof that $\Phi$ is surjective and then complete the picture by calculating the ideal of relations explicitly. As an application, we then use this presentation to show that $\text{Gr}(n,2)$ is isomorphic to a fine moduli space of certain stable $A$-modules, just as $\mathbb{P}^n$ can be recovered from the endomorphism algebra of Beilinson's tilting bundle $\bigoplus_{0\leq i\leq n}\mathcal{O}_{\mathbb{P}^n}(i)$.
Fast and accurate integration of geodesics in Kerr spacetimes is an important tool in modeling the orbits of stars and the transport of radiation in the vicinities of black holes. Most existing integration algorithms employ Boyer-Lindquist coordinates, which have coordinate singularities at the event horizon and along the poles. Handling the singularities requires special numerical treatment in these regions, often slows down the calculations, and may lead to inaccurate geodesics. We present here a new general-purpose geodesic integrator, GRay2, that overcomes these issues by employing the Cartesian form of Kerr-Schild coordinates. By performing particular mathematical manipulations of the geodesic equations and several optimizations, we develop an implementation of the Cartesian Kerr-Schild coordinates that outperforms calculations that use the seemingly simpler equations in Boyer-Lindquist coordinates. We also employ the OpenCL framework, which allows GRay2 to run on multi-core CPUs as well as on a wide range of GPU hardware accelerators, making the algorithm more versatile. We report numerous convergence tests and benchmark results for GRay2 for both time-like (particle) and null (photon) geodesics.
We construct solutions to the Einstein equations for asymptotically locally Anti-de Sitter spacetimes with four, five, and six dimensional Reissner-Nordstr\"om boundary metrics. These spacetimes are gravitational duals to "jammed" CFTs on those backgrounds at infinite N and strong coupling. For these spacetimes, we calculate the boundary stress tensor as well as compute entanglement entropies for ball shaped regions as functions of the boundary black hole temperature $T_{BH}$. From this, we see how the CFT prevents heat flow from the black hole to the vacuum at spatial infinity. We also compute entanglement entropies for a three dimensional boundary black hole using the AdS C-metric. We compare our results to previous work done in similar spacetimes.
Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit an instability at low temperature. We find an explicit solution that represents a charged asymptotically Anti-de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in Anti-de Sitter space in which the backreaction on the geometry can be solved analytically.
We give a heuristic argument supporting conjectures of Bhargava on the asymptotics of the number of $S_n$-number fields having bounded discriminant. We then make our arguments rigorous in the case $n=3$ giving a new elementary proof of the Davenport-Heilbronn theorem. Our basic method is to count elements of small height in $S_n$-fields while carefully keeping track of the index of the monogenic ring that they generate.
The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.
This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system.
The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this work, we analyse the application of nonlinear witnesses to the verification of entanglement, and we demonstrate experimentally that nonlinear witnesses perform significantly better than linear witnesses. Specifically, we demonstrate that a single non- linear entanglement witness is able to determine to a high degree of certainty that a mixed state containing orbital angular momentum (OAM) entanglement of specific forms is entangled for any relative phase and sufficient fidelity. This is a significant improvement over linear witnesses, which cannot provide the same level of performance. We envisage that nonlinear witnesses and our method of state preparation will have further uses in areas of quantum science such as superdense coding and quantum key distribution.
IceCube is a cubic-kilometer Cherenkov detector installed in deep ice at the geographic South Pole. IceCube's surface array, IceTop, measures the electromagnetic signal and mainly low-energy muons from extensive air showers above several 100 TeV primary energy, with shower bundles and high-energy muons detected by the in-ice detector IceCube. In combination, the in-ice detector and IceTop provide unique opportunities to study cosmic rays in detail with large statistics. This contribution summarizes recent results from these studies. In addition, the IceCube-Upgrade will include a considerable enhancement of the surface detector through the installation of scintillation detectors and radio antennas and possibly small air-Cherenkov telescopes. We will discuss the results of the prototype detectors installed at the South Pole and the prospects of this enhancement as well as the surface array planned for IceCube-Gen2.
We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.
Difficulties associated with the integration of liquids into a UHV environment make surface-science style studies of mineral dissolution particularly challenging. Recently, we developed a novel experimental setup for the UHV-compatible dosing of ultrapure liquid water, and studied its interaction with TiO2 and Fe3O4 surfaces. Here, we describe a simple approach to vary the pH through the partial pressure of CO2 (pCO2) in the surrounding vacuum chamber, and use this to study how these surfaces react to an acidic solution. The TiO2(110) surface is unaffected by the acidic solution, except for a small amount of carbonaceous contamination. The Fe3O4(001)-(rt2 x rt2)R45 surface begins to dissolve at a pH 4.0-3.9 (pCO2 = 0.8-1 bar) and, although it is significantly roughened, the atomic-scale structure of the Fe3O4(001) surface layer remains visible in scanning tunneling microscopy (STM) images. X-ray photoelectron spectroscopy (XPS) reveals that the surface is chemically reduced, and contains a significant accumulation of bicarbonate (HCO3-) species. These observations are consistent with Fe(II) being extracted by bicarbonate ions, leading to dissolved iron bicarbonate complexes (Fe(HCO3)2), which precipitate onto the surface when the water evaporates.
This paper presents a view-guided solution for the task of point cloud completion. Unlike most existing methods directly inferring the missing points using shape priors, we address this task by introducing ViPC (view-guided point cloud completion) that takes the missing crucial global structure information from an extra single-view image. By leveraging a framework that sequentially performs effective cross-modality and cross-level fusions, our method achieves significantly superior results over typical existing solutions on a new large-scale dataset we collect for the view-guided point cloud completion task.
The influence of bond randomness on long range magnetic ordering in the weakly coupled S = 1/2 antiferromagnetic spin chain materials Cu(py)2(Cl1-xBrx)2 is studied by muon spin rotation and bulk measurements. Disorder is found to have a strong effect on the ordering temperature TN, and an even stronger one on the saturation magnetization m0, but considerably more so in the effectively lower-dimensional Br-rich materials. The observed behavior is attributed to Random Singlet ground states of individual spin chains, but remains in contradiction with chain mean field theory predictions. In this context, we discuss the possibility of a universal distribution of ordered moments in the weakly coupled Random Singlet chains model.
We are concerned with solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$, $x\in \mathbb{R}^N$, that are defined for all positive and negative time. If the exponent $p$ is greater or equal to the Joseph-Lundgren exponent $p_c$ and $|u|$ stays below some positive radially symmetric steady state, under a mild condition on the behaviour of $u$ as $|x|\to \infty$, we show that $u$ is independent of time. Our method of proof uses Serrin's sweeping principle, based on the strong maximum principle, applied to the linearized equation for $u_t$. Our result covers that of Pol\'{a}\v{c}ik and Yanagida [JDE (2005)] who had further assumed that the solution stays above some positive radial steady state and $p>p_c$. In contrast, they relied on the use of similarity variables and invariant manifold ideas. Remarkably, to the best of our knowledge, a corresponding Liouville property was previously missing for $p =p_c$. We emphasize that such Liouville type theorems imply the quasiconvergence of a class of solutions to the corresponding Cauchy problem. As our viewpoint originates from the study of elliptic problems, we can prove new rigidity results for the corresponding steady state problem that are motivated by the aforementioned ones for the parabolic flow.
In this paper we consider the classical and Erlang(2) risk processes when the inter-claim times and claim amounts are dependent. We assume that the dependence structure is defined through a Farlie-Gumbel-Morgenstern (FGM) copula and show that the methods used to derive results in the classical risk model can be modified to derive results in a dependent risk process. We find expressions for the survival probability and the probability of maximum surplus before ruin.
Let $K$ be a field of characteristic 0. Fix integers $r,d$ coprime with $r \geq 2$. Let $X_K$ be a smooth, projective, geometrically connected curve of genus $g \geq 2$ defined over K. Assume there exists a line bundle $L_K$ on $X_K$ of degree $d$. In this article we prove the existence of a stable locally free sheaf on $X_K$ with rank $r$ and determinant $L_K$. This trivially proves the $C_1$ conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.
We investigate the reciprocity law, studied by Conrey~\cite{Con07} and Young~\cite{You11a}, for the second moment of Dirichlet L-functions twisted by $\chi(a)$ modulo a prime $q$. We show that the error term in this reciprocity law can be extended to a continuous function of $a/q$ with respect to the real topology. Furthermore, we extend this reciprocity result, proving an exact formula involving also shifted moments.   We also give an expression for the twisted second moment involving the coefficients of the continued fraction expansion of $a/q$, and, consequently, we improve upon a classical result of Selberg on the second moment of Dirichlet L-functions with two twists.   Finally, we obtain a formula connecting the shifted second moment of the Dirichlet $L$-functions with the Estermann function. In particular cases, this result can be used to obtain some simple explicit exact formulae for the moments.
Jantzen-Seitz partitions are those $p$-regular partitions of~$n$ which label $p$-modular irreducible representations of the symmetric group $S_n$ which remain irreducible when restricted to $S_{n-1}$; they have recently also been found to be important for certain exactly solvable models in statistical mechanics. In this article we study their combinatorial properties via a detailed analysis of their residue symbols; in particular the $p$-cores of Jantzen-Seitz partitions are determined.
The local magnetic moment of Ti:ZnO is calculated from first principles by using the corrected-band-gap scheme (CBGS). The results shows that the system is magnetic with the magnetization of 0.699 $\mu_B$ per dopant. The origin of the local magnetic moment is considered to be the impurity band partially occupied by the donor electrons in the conduction band. Further, the impacts of applying Hubbard U to Ti-d orbital on the magnetic moment have been investigated.
Experimental measurement of the elliptic flow parameter $v_2$ and hydrodynamic model together showed that thermalization in the central region at the Relativistic Heavy Ion Collider to be perplexingly fast. This is a mystery in itself since none of the numerical perturbative QCD models are able to achieve such a feat. By exploiting a theoretical oversight on collinear processes in an out-of-equilibrium system it is argued that, in the bottom-up thermalization scenario, equilibration can proceed at a higher rate than what is expected in the conventional perturbative QCD picture.
We discuss the kinematics of the particles that make up a Reggeon in field theory, using the terminology of the Soft Collinear Effective Theory (SCET). Reggeization sums a series of strongly-ordered collinear emissions resulting in an overall Reggeon exchange that falls in the Glauber or Coulomb kinematic region. This is an extremely multi-scale problem and appears to fall outside of the usual organizing scheme of SCET.
In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial $G_\lambda(x;q)$ in some special cases. We associate a weighted graph $\Pi$ to $\lambda$ and we use it to express a linear relation among LLT polynomials. We apply this relation to prove an explicit combinatorial Schur-positive expansion of $G_\lambda(x;q)$ whenever $\Pi$ is triangle-free. We also prove that the largest power of $q$ in the LLT polynomial is the total edge weight of our graph.
We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.
The site-diluted Ising model has been investigated using an improved microcanonical algorithm from Creutz Cellular Automaton. For a microcanonical algorithm, the basic problem is to estimate the correct temperatures using average values of the kinetic energy in the simulations of site-diluted Ising model. In this study, the average kinetic energy has been re-described with an expression dependent on dilution x=1-p. The values of the temperature have been calculated using the new expression and the critical temperatures have been estimated from the peaks of specific heat for each value of dilution x. The obtained phase transition line (kT_{C}(p)/J, p) is in good agreement with functional prediction for the site-diluted Ising model. The simulations were carried out on a square lattice with periodic boundary conditions.