ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane.   These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the reference hyperplane.   Remarkably, the oscillations of the interfaces with respect to the reference hyperplane are bounded by a universal constant times the periodicity scale of the medium.   This geometric property allows us to establish, in the limit, the existence of planelike nonlocal minimal surfaces in a periodic structure.   The proofs rely on new optimal density and energy estimates. In particular, roughly speaking, the energy of phase transition minimizers is controlled, both from above and below, by the energy of one-dimensional transition layers.
In this paper we introduce a new modification of the Jacobi-Perron algorithm in three dimensional case and prove its periodicity for the case of totally-real conjugate cubic vectors. This provides an answer in the totally-real case to the question son algebraic periodicity for cubic irrationalities posed in 1849 by Ch.~Hermite.
Here we discuss the possibility of super-massive binary black hole (SMBBH) detection, using the shifts of the broad lines emitted from a binary system. We perform a number of simulations of shapes and shifts of $H_{\beta}$ lines emitted from SMBBHs, taking into account the emission from two different regions located around both black holes, and kinematical effects which should be present in a SMBBH. In the model we connect the parameters of the lines with the mass of black holes and find that the peak shift depends, not only on kinematical effects of system rotation and black hole mass ratio, but it is also a function of the individual masses of the two black holes (BHs).
The exact analytic solutions of the energy eigenvalue equation of the system consisting of a free electron and one mode of the quantized radiation field are used for studying the physical meaning of a class of number-phase minimum uncertainty states. The states of the mode which minimize the uncertainty product of the photon number and the Susskind and Glogower (1964) cosine operator have been obtained by Jackiw (1968). However, these states have so far been remained mere mathematical constructions without any physical significance. It is proved that the most fundamental interaction in quantum electrodynamics - namely the interaction of a free electron with a mode of the quantized radiation field - leads quite naturally to the generation of the mentioned minimum uncertainty states. It is shown that from the entangled photon-electron states developing from a highly excited number state, due to the interaction with a Gaussian electronic wave packet, the minimum uncertainty states of Jackiw's type can be constructed. In the electron's coordinate representation the physical meaning of the expansion coefficients of these states are the joint probability amplitudes of simultaneous detection of an electron and of a definite number of photons. The joint occupation probabilities in these states preserve their functional form as time elapses, but they vary from point to point in space-time, depending on the location of the detected electron. An analysis of the entanglement entropies derived from the photon number distribution and from the electron's density operator is given.
A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions.
Hot Dust-Obscured Galaxies (Hot DOGs) are hyperluminous ($L_{\mathrm{8-1000\,\mu m}}>10^{13}\,\mathrm{L_\odot}$) infrared galaxies with extremely high (up to hundreds of K) dust temperatures. The sources powering both their extremely high luminosities and dust temperatures are thought to be deeply buried and rapidly accreting supermassive black holes (SMBHs). Hot DOGs could therefore represent a key evolutionary phase in which the SMBH growth peaks. X-ray observations can be used to study their obscuration levels and luminosities. In this work, we present the X-ray properties of the 20 most-luminous ($L_{\mathrm{bol}}\gtrsim10^{14}\, L_\odot$) known Hot DOGs at $z=2-4.6$. Five of them are covered by long-exposure ($10-70$ ks) Chandra and XMM-Newton observations, with three being X-ray detected, and we study their individual properties. One of these sources (W0116$-$0505) is a Compton-thick candidate, with column density $N_H=(1.0-1.5)\times10^{24}\,\mathrm{cm^{-2}}$ derived from X-ray spectral fitting. The remaining 15 Hot DOGs have been targeted by a Chandra snapshot (3.1 ks) survey. None of these 15 is individually detected; therefore we applied a stacking analysis to investigate their average emission. From hardness-ratio analysis, we constrained the average obscuring column density and intrinsic luminosity to be log$N_H\,\mathrm{[cm^{-2}]}>23.5$ and $L_X\gtrsim10^{44}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$, which are consistent with results for individually detected sources. We also investigated the $L_X-L_{6\mu\mathrm{m}}$ and $L_X-L_{bol}$ relations, finding hints that Hot DOGs are typically X-ray weaker than expected, although larger samples of luminous obscured QSOs are needed to derive solid conclusions.
Modifications to the gravitational potential affect the nonlinear gravitational evolution of large scale structures in the Universe. To illustrate some generic features of such changes, we study the evolution of spherically symmetric perturbations when the modification is of Yukawa type; this is non-trivial, because we should not and do not assume that Birkhoff's theorem applies. We then show how to estimate the abundance of virialized objects in such models. Comparison with numerical simulations shows reasonable agreement: When normalized to have the same fluctuations at early times, weaker large scale gravity produces fewer massive halos. However, the opposite can be true for models that are normalized to have the same linear theory power spectrum today, so the abundance of rich clusters potentially places interesting constraints on such models. Our analysis also indicates that the formation histories and abundances of sufficiently low mass objects are unchanged from standard gravity. This explains why simulations have found that the nonlinear power-spectrum at large k is unaffected by such modifications to the gravitational potential. In addition, the most massive objects in CMB-normalized models with weaker gravity are expected to be similar to the high-redshift progenitors of the most massive objects in models with stronger gravity. Thus, the difference between the cluster and field galaxy populations is expected to be larger in models with stronger large-scale gravity.
We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state of the process. Our method is based on an embedding into a Hilbert space of functions which allows to represent the solution of the Volterra equation as the boundary value of a solution to a stochastic partial differential equation. We first gather abstract results and give more detailed conditions in more specific function spaces.
The thermal evolution of the intergalactic medium (IGM) can serve as a sensitive probe of cosmological heat sources and sinks. We employ it to limit interactions between dark matter and baryons. After reionization the IGM temperature is set by the balance between photoheating and adiabatic cooling. We use measurements of the IGM temperature from Lyman-$\alpha$-forest data to constrain the cross-section $\sigma$ between dark matter and baryons, finding $\sigma < 10^{-20}$ cm$^2$ for dark-matter masses $m_\chi\leq 1$ GeV. This provides the first direct constraint on scattering between dark matter and baryons at redshift $z\sim5$.
Photometric observations of the spectroscopically confirmed $z\approx 9.1$ galaxy MACS1149-JD1 have indicated the presence of a prominent Balmer break in its spectral energy distribution, which may be interpreted as due to very large fluctuations in its past star formation activity. In this paper, we investigate to what extent contemporary simulations of high-redshift galaxies produce star formation rate variations sufficiently large to reproduce the observed Balmer break of MACS1149-JD1. We find that several independent galaxy simulations are unable to account for Balmer breaks of the inferred size, suggesting that MACS1149-JD1 either must be a very rare type of object or that our simulations are missing some key ingredient. We present predictions of spectroscopic Balmer break strength distributions for $z\approx 7-9$ galaxies that may be tested through observations with the upcoming James Webb Space Telescope and also discuss the impact that various assumptions on dust reddening, Lyman continuum leakage and deviations from a standard stellar initial mass function would have on the results.
The tangential shear signal receives contributions from physical scales in the galaxy-matter correlation function well below the transverse scale at which it is measured. Since small scales are difficult to model, this non-locality has generally required stringent scale cuts or new statistics for cosmological analyses. Using the fact that uncertainty in these contributions corresponds to an uncertainty in the enclosed projected mass around the lens, we provide an analytic marginalization scheme to account for this. Our approach enables the inclusion of measurements on smaller scales without requiring numerical sampling over extra free parameters. We extend the analytic marginalization formalism to retain cosmographic ("shear-ratio") information from small-scale measurements that would otherwise be removed due to modeling uncertainties, again without requiring the addition of extra sampling parameters. We test the methodology using simulated likelihood analysis of a DES Year 5-like galaxy-galaxy lensing and galaxy clustering datavector. We demonstrate that we can remove parameter biases due to the presence of an un-modeled 1-halo contamination of the galaxy-galaxy lensing signal, and use the shear-ratio information on small scales to improve cosmological parameter constraints.
We show that, given a projective regular function f on a smooth quasi-projective variety over C, the corresponding cohomology groups of the algebraic de Rham complex with twisted differential d-df and of the complex of algebraic forms with differential df have the same dimension (a result announced by Barannikov and Kontsevitch). We generalize the result to de Rham complexes with coefficients in a mixed Hodge Module.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions $2t\leq U\leq 10t$, temperatures $0.2t\lesssim T\lesssim t$ and electron concentrations $0.7\lesssim\bar{n}\leq1$ with $t$ the intersite hopping constant. For all considered $U$ the system exhibits a transition to the long-range antiferromagnetic order at $T_{\rm AF}\approx 0.2t$. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the $U$-$T$ plane, the curve separating metallic solutions passes from $U\approx6t$ at the highest temperatures to $U=2t$ at $T\approx T_{\rm AF}$ for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low $T$, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for $U\gtrsim6t$ to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for $U\lesssim3t$. For $T\approx T_{\rm AF}$ and $U\gtrsim 7t$ doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband.
Small-angle scattering (SAS) data which show a succession of power-law decays with decreasing values of scattering exponents, can be described in terms of fractal structures with positive Lebesgue measure (fat fractals). In this work we present a theoretical model for fat fractals and show how one can extract structural information about the underlying fractal using SAS method, for the well known fractals existing in the literature: Vicsek and Menger sponge. We calculate analytically the fractal structure factor and study its properties in momentum space. The models allow us to obtain the fractal dimension at each structural level inside the fractal, the number of particles inside the fractal and about the most common distances between the center of mass of the particles.
Twisted rapid passage is a type of non-adiabatic rapid passage that gives rise to controllable quantum interference effects that were first observed experimentally in 2003. We show that twisted rapid passage sweeps can be used to implement a universal set of quantum gates that operate with high-fidelity. For each gate in the universal set, sweep parameter values are provided which simulations indicate will yield a quantum gate with error probability P_{e} < 10**(-4). Note that all gates in this universal set are driven by a **single** type of control field (twisted rapid passage), and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold P_{a} ~ 10**(-4). The simulations suggest that the universal gate set produced by twisted rapid passage shows promise for use in a fault-tolerant scheme for quantum computing.
We have calculated partial final-state resolved radiative recombination (RR) rate coefficients from the initial ground and metastable levels of all elements up to and including Zn, plus Kr, Mo, and Xe, for all isoelectronic sequences up to Na-like forming Mg-like. The data are archived according to the Atomic Data and Analysis Structure (ADAS) data class adf48, which spans a temperature range of z^2(10^1 - 10^7)K, where z is the initial ion charge. Fits to total rate coefficients have been determined, for both the ground and metastable levels, and those for the ground are presented here. Comparison is made both with previous RR rate coefficients and with (background) R-matrix photoionization cross sections. This RR database complements a DR database already produced and both are being used to produce updated ionization balances for both (electron) collisionally ionized and photoionized plasmas.
In this papers, we study the geometric and arithmetic properties of the theta divisor associated to the sheaf of locally exact differential forms over a curve in positive characteristic. In this published version, we prove a stronger version of the main result of chapiter 5.
These are the lecture notes from a five-hour mini-course given at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. Their aim is to give an overview of Serre's modularity conjecture and of its proof by Khare, Wintenberger, and Kisin, as well as of the results of other mathematicians that played an important role in the proof. Along the way we remark on some recent (as of 2012) work concerning generalizations of the conjecture.
Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena.
We prove a necessary and sufficient condition for a symmetric association scheme to be a Q-polynomial scheme.
We propose an efficient method for non-rigid surface tracking from monocular RGB videos. Given a video and a template mesh, our algorithm sequentially registers the template non-rigidly to each frame. We formulate the per-frame registration as an optimization problem that includes a novel texture term specifically tailored towards tracking objects with uniform texture but fine-scale structure, such as the regular micro-structural patterns of fabric. Our texture term exploits the orientation information in the micro-structures of the objects, e.g., the yarn patterns of fabrics. This enables us to accurately track uniformly colored materials that have these high frequency micro-structures, for which traditional photometric terms are usually less effective. The results demonstrate the effectiveness of our method on both general textured non-rigid objects and monochromatic fabrics.
We discuss the model selection problem for inflationary cosmology. We couple ModeCode, a publicly-available numerical solver for the primordial perturbation spectra, to the nested sampler MultiNest, in order to efficiently compute Bayesian evidence. Particular attention is paid to the specification of physically realistic priors, including the parametrization of the post-inflationary expansion and associated thermalization scale. It is confirmed that while present-day data tightly constrains the properties of the power spectrum, it cannot usefully distinguish between the members of a large class of simple inflationary models. We also compute evidence using a simulated Planck likelihood, showing that while Planck will have more power than WMAP to discriminate between inflationary models, it will not definitively address the inflationary model selection problem on its own. However, Planck will place very tight constraints on any model with more than one observationally-distinct inflationary regime -- e.g. the large- and small-field limits of the hilltop inflation model -- and put useful limits on different reheating scenarios for a given model.
As an application of the renormalization method introduced by the second author we give a causal definition of the phase of the quantum scattering matrix for fermions in external Yang-Mills potentials. The phase is defined using parallel transport along the path of renormalized time evolution operators. The time evolution operators are elements of the restricted unitary group $U_{res}$ of Pressley and Segal. The central extension of $U_{res}$ plays a central role.
We obtain new bounds for short sums of isotypic trace functions associated to some sheaf modulo prime $p$ of bounded conductor, twisted by the Mobius function and also by the generalised divisor function. These trace functions include Kloosterman sums and several other classical number theoretic objects. Our bounds are nontrivial for intervals of length at least $p^{1/2+\varepsilon}$ with an arbitrary fixed $\varepsilon >0$, which is shorter than the length at least $p^{3/4+\varepsilon}$ in the case of the Mobius function and at least $p^{2/3+\varepsilon}$ in the case of the divisor function required in recent results of {\'E}.~Fouvry, E.~Kowalski and P.~Michel (2014) and E.~Kowalski, P. ~Michel and W.~Sawin (2018), respectively.
For many decades, the magnetic saturation of, e.g. hard metals (HM) such as WC-Co-based cemented carbides, has been used as process and quality control in industry to ensure consistency of product properties. In an urge of replacing cobalt as a binder phase, a demand on understanding the magnetic response as a function of composition on the atomic scale is growing. In this paper, a theoretical description of the measured weight specific magnetic saturation of hard metals as a function of the tungsten weight fraction present in the cobalt binder phase, based on first-principle calculations, has been established for standard WC-Co. The predicted magnetic saturation agrees well with the experimental one. Furthermore, it is proposed that the theoretical description can be extended to alternative and more complex binder phases which allows to transfer the production control to those hard metals.
Modeling the amplitudes and shapes of the X-ray pulsations observed from hot, rotating neutron stars provides a direct method for measuring neutron-star properties. This technique constitutes an important part of the science case for the forthcoming NICER and proposed LOFT X-ray missions. In this paper, we determine the number of distinct observables that can be derived from pulse profile modeling and show that using only bolometric pulse profiles is insufficient for breaking the degeneracy between inferred neutron-star radius and mass. However, we also show that for moderately spinning (300-800 Hz) neutron stars, analysis of pulse profiles in two different energy bands provides additional constraints that allow a unique determination of the neutron-star properties. Using the fractional amplitudes of the fundamental and the second harmonic of the pulse profile in addition to the amplitude and phase difference of the spectral color oscillations, we quantify the signal-to-noise ratio necessary to achieve a specified measurement precision for neutron star radius. We find that accumulating 10^6 counts in a pulse profile is sufficient to achieve a <5% uncertainty in the neutron star radius, which is the level of accuracy required to determine the equation of state of neutron-star matter. Finally, we formally derive the background limits that can be tolerated in the measurements of the various pulsation amplitudes as a function of the system parameters.
We describe a theoretical study of the role of adsorbate interactions in island nucleation and growth, using Ag/Pt(111) heteroepitaxy as an example.   From density-functional theory, we obtain the substrate-mediated Ag adatom pair interaction and we find that, past the short range, a repulsive ring is formed about the adatoms. The magnitude of the repulsion is comparable to the diffusion barrier. In kinetic Monte Carlo simulations, we find that the repulsive interactions lead to island densities over an order of magnitude larger than those predicted by nucleation theory and thus identify a severe limitation of its applicability.