ShantanuT01/DACTYL-Pretraining huggingface dataset:
The main goal of this paper is to show that the blow up phenomenon (the explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls $\alpha (t)$ ($i.e.$ only dependent on time) in such a way that the corresponding solution be well defined (as element of $\rL_{loc}^{1}(0,+\infty :\rX)$, for some functional space $\rX$) after the explosion time. We start by considering the case of an ordinary differential equation with a superlinear term and show that the controlled explosion property holds by using a delayed control (built through the solution of the problem and by generalizing the {\em nonlinear variation of constants formula}, due to V.M. Alekseev in 1961, to the case of {\em neutral delayed equations} (since the control is only in the space $\rW_{loc}^{-1,q\prime }(0,+\infty :\RR )$, for some $q>1$)$.$ We apply those arguments to the case of an evolution semilinear problem in which the differential equation is a semilinear elliptic equation with a superlinear absorption and the boundary condition is dynamic and involves the forcing superlinear term giving rise to the blow up phenomenon. We prove that, under a suitable balance between the forcing and the absorption terms, the blow up takes place only on the boundary of the spatial domain which here is assumed to be a ball $\rB_{\rR}$ and for a constant as initial datum.
In this paper we consider the Anderson Hamiltonian with white noise potential on the box $[0,L]^2$ with Dirichlet boundary conditions. We show that all the eigenvalues divided by $\log L$ converge as $L\rightarrow \infty$ almost surely to the same deterministic constant, which is given by a variational formula.
Riemannian and contact geometry formalisms are used to study the fundamental equation of electromagnetic radiation-like systems, obeying a Stefan-Boltzmann's-like law. The vanishing of metric determinant is used for classifying what kind of systems can not represent a possible generalization of blackbody-like systems. In addition, thermodynamic curvature scalar $\mathcal{R}$ is evaluated for a thermodynamic metric, giving $\mathcal{R}=0$, which validates the non-interaction hypothesis stating that the scalar curvature vanishes for non-interacting systems.
We study analytically the Cauchy horizon singularity inside spherically-symmetric charged black holes, coupled to a spherical self-gravitating, minimally-coupled, massless scalar field. We show that all causal geodesics terminate at the Cauchy horizon at a null singularity, which is weak according to the Tipler classification. The singularity is also deformationally-weak in the sense of Ori. Our results are valid at arbitrary points along the null singularity, in particular at late retarded times, when non-linear effects are crucial.
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. Hence, the configurational subsystem is non-extensive in the sense of Tsallis. One of the consequences of this observation is that the thermodynamics of the configurational subsystem is uniquely determined up to a scaling function. As an example we consider a system of non-interacting harmonic oscillators. In this example, the scaling function can be determined from the requirement that in the limit of large systems the microcanonical temperature of the configurational subsystem should coincide with that of the canonical ensemble. The result suggests that Renyi's entropy function is the relevant one rather than that of Tsallis.
We generalise the finite range momentum and density dependent Seyler-Blanchard nucleon-nucleon effective interaction to the case of interaction between two baryons. This effective interaction is then used to describe dense hadronic matter relevant to neutron stars in the nonrelativistic Thomas-Fermi approach. We investigate the behaviour of nuclear symmetry energy in dense nuclear and hyperon matter relevant to neutron stars. It is found that the nuclear symmetry energy always increases with density in hyperon matter unlike the situation in nuclear matter. This rising characteristic of the symmetry energy in presence of hyperons may have significant implications on the mass-radius relationship and the cooling properties of neutron stars. We have also noted that with the appearance of hyperons, the equation of state calculated in this model remains causal at high density.
We explore the effects of active galactic nuclei (AGN) and star formation activity on the infrared (0.3-1000 microns) spectral energy distributions of luminous infrared galaxies from z = 0.5 to 4.0. We have compiled a large sample of 151 galaxies selected at 24 microns (S24 > 100 uJy) in the GOODS-N and ECDFS fields for which we have deep Spitzer IRS spectroscopy, allowing us to decompose the mid-IR spectrum into contributions from star formation and AGN activity. A significant portion (~25%) of our sample is dominated by an AGN in the mid-IR. Based on the mid-IR classification, we divide our full sample into four sub-samples: z~1 star-forming (SF) sources; z~2 SF sources; AGN with clear 9.7 micron silicate absorption; and AGN with featureless mid-IR spectra. From our large spectroscopic sample and wealth of multi-wavelength data, including deep Herschel imaging at 100, 160, 250, 350, and 500 microns, we use 95 galaxies with complete spectral coverage to create a composite spectral energy distribution (SED) for each sub-sample. We then fit a two-temperature component modified blackbody to the SEDs. We find that the IR SEDs have similar cold dust temperatures, regardless of the mid-IR power source, but display a marked difference in the warmer dust temperatures. We calculate the average effective temperature of the dust in each sub-sample and find a significant (~20 K) difference between the SF and AGN systems. We compare our composite SEDs to local templates and find that local templates do not accurately reproduce the mid-IR features and dust temperatures of our high redshift systems. High redshift IR luminous galaxies contain significantly more cool dust than their local counterparts. We find that a full suite of photometry spanning the IR peak is necessary to accurately account for the dominant dust temperature components in high redshift IR luminous galaxies.
The evolution of electromagnetic and Dirac perturbations in the spacetime geometry of Kehagias-Sfetsos(KS) black hole in the deformed Horava-Lifshitz(HL) gravity is investigated and the associated quasinormal modes are evaluated using time domain integration and WKB methods. We find a considerable deviation in the nature of field evolution in HL theory from that in the Schwarzschild spacetime and QNMs region extends over a longer time in HL theory before the power-law tail decay begins. The dependence of the field evolution on the HL parameter $\alpha$ are studied. In the time domain picture we find that the length of QNM region increases with $\alpha$. But the late time decay of field follows the same power-law tail behavior as in the case of Schwarzschild black hole.
The effect of nonconservative current-induced forces on the ions in a defect-free metallic nanowire is investigated using both steady-state calculations and dynamical simulations. Non-conservative forces were found to have a major influence on the ion dynamics in these systems, but their role in increasing the kinetic energy of the ions decreases with increasing system length. The results illustrate the importance of nonconservative effects in short nanowires and the scaling of these effects with system size. The dependence on bias and ion mass can be understood with the help of a simple pen and paper model. This material highlights the benefit of simple preliminary steady-state calculations in anticipating aspects of brute-force dynamical simulations, and provides rule of thumb criteria for the design of stable quantum wires.
Taylor-Wiles type lifting theorems allow one to deduce that for $\rho$ a "sufficiently nice" $l$-adic representation of the absolute Galois group of a number field whose semi-simplified reduction modulo $l$, denoted $\overline{\rho}$, comes from an automorphic representation then so does $\rho$. The recent lifting theorems of Barnet-Lamb-Gee-Geraghty-Taylor impose a technical condition, called \emph{$m$-big}, upon the residual representation $\overline{\rho}$. Snowden-Wiles proved that for a sufficiently irreducible compatible system of Galois representations, the residual images are \emph{big} at a set of places of Dirichlet density $1$. We demonstrate the analogous result in the \emph{$m$-big} setting using a mild generalization of their argument.
The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the B\"uttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter values for optimal performance of the heat engine and heat pump. Our results qualitatively differ from approaches based on the overdamped model. The behavior of the heat engine and heat pump, in the linear response regime is examined under finite time conditions and we find that the efficiency is lower than that of an endoreversible engine working under the same condition. Finally, we investigate the role of different potential and temperature profiles to enhance the efficiency of the system. Our simulations show that optimizing the potential and temperature profile leads only to a marginal enhancement of the system performance due to the large entropy production via the Brownian particle's kinetic energy.
Weakly supervised Referring Expression Grounding (REG) aims to ground a particular target in an image described by a language expression while lacking the correspondence between target and expression. Two main problems exist in weakly supervised REG. First, the lack of region-level annotations introduces ambiguities between proposals and queries. Second, most previous weakly supervised REG methods ignore the discriminative location and context of the referent, causing difficulties in distinguishing the target from other same-category objects. To address the above challenges, we design an entity-enhanced adaptive reconstruction network (EARN). Specifically, EARN includes three modules: entity enhancement, adaptive grounding, and collaborative reconstruction. In entity enhancement, we calculate semantic similarity as supervision to select the candidate proposals. Adaptive grounding calculates the ranking score of candidate proposals upon subject, location and context with hierarchical attention. Collaborative reconstruction measures the ranking result from three perspectives: adaptive reconstruction, language reconstruction and attribute classification. The adaptive mechanism helps to alleviate the variance of different referring expressions. Experiments on five datasets show EARN outperforms existing state-of-the-art methods. Qualitative results demonstrate that the proposed EARN can better handle the situation where multiple objects of a particular category are situated together.
This paper studies probabilistic mean-field models for interacting bosons at a positive temperature in the thermodynamic limit with random particle density. In particular, we prove large deviation principles for empirical cycle counts in all our models, and as such generalise recent work in \cite{ACK} where upper and lower large deviation bounds do not match. Namely, on the one hand we generalise to the so-called grand canonical ensemble, and on the other hand, we consider classes of interaction potentials depending on the cycle counts which are not restricted to be positive. Our large deviation results provide representation formulae for the thermodynamic limit of the pressure which in turn leads to proving Bose-Einstein-condensation (BEC) in all our models.   A primary focus and novelty is the pressure representation via extended large deviation analysis for the so-called hard-sphere, or HYL-model (Huang-Yang-Luttinger) studied in \cite{Lew86}. This model has negative counter terms in the Hamiltonian and shows BEC depending on the coupling constants.
We report a first principles theoretical study of the surface relaxation and lattice dynamics of the Cu(211) surface using the plane wave pseudopotential method. We find large atomic relaxations for the first several atomic layers near the step edges on this surface, and a substantial step-induced renormalization of the surface harmonic force constants. We use the results to study the harmonic fluctuations around the equilibrium structure and find three new step-derived features in the zone center vibrational spectrum. Comparison of these results with previous theoretical work and weith experimental studies using inelastic He scattering are reported.
We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series.
In the present study, we have investigated the impact of the tensor force on fission paths, in particular the symmetric and asymmetric barriers in 230 Th, 226 Th, 222 Th and 216 Th isotopes which display an asymmetric to symmetric fission transition. This analysis has been performed within the HFB approach with (Q 20 ,Q 30 ,Q 40 ) as collective variable constraints, using the D1ST2a Gogny+tensor term interaction and comparing to the standard D1S Gogny interaction results. The effects from the tensor term on the potential energy surface landscape, and especially on barrier heights and its topology by opening a new valley in agreement with experimental data, are found to be crucial in the description of exotic actinide fission. We conclude that a tensor term should be integrated to the long range part of the effective interaction for a better description of the fission.
We present a novel approach to reference-based super-resolution (RefSR) with the focus on dual-camera super-resolution (DCSR), which utilizes reference images for high-quality and high-fidelity results. Our proposed method generalizes the standard patch-based feature matching with spatial alignment operations. We further explore the dual-camera super-resolution that is one promising application of RefSR, and build a dataset that consists of 146 image pairs from the main and telephoto cameras in a smartphone. To bridge the domain gaps between real-world images and the training images, we propose a self-supervised domain adaptation strategy for real-world images. Extensive experiments on our dataset and a public benchmark demonstrate clear improvement achieved by our method over state of the art in both quantitative evaluation and visual comparisons.
We calculate total masses and radii of neutron stars (NS) for pure neutron matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We use realistic nucleon-nucleon (NN) interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.
We present a comparison between accurate \textit{ab initio} calculations and a high-quality experimental data set (1986-2002) of electric-field gradients and magnetic hyperfine fields of Cd at different sites on Ni, Cu, Pd and Ag surfaces. Experiments found a systematic rule to assign surface sites on (100) and (111) surfaces based on the main component of the electric-field gradient, a rule that does not work for (110) surfaces. Our calculations show that this particular rule is a manifestation of a more general underlying systematic behavior. When looked upon from this point of view, (100), (111) \emph{and} (110) surfaces behave in precisely the same way. The experimentally observed parabolic coordination number dependence of the Cd magnetic hyperfine field at Ni surfaces is verified as a general trend, but we demonstrate that individual cases can significantly deviate from it. It is shown that the hyperfine fields of other 5sp impurities at Ni surfaces have their own, typical coordination number dependence. A microscopic explanation for the different dependencies is given in terms of the details of the s-DOS near the Fermi level.
Transport simulations including in-medium properties derived in a microscopic pi + nucleon-hole + delta-hole model in infinite nuclear matter are presented. In-medium pion dispersion relations, partial delta decay widths, pion absorption cross sections and delta cross sections are incorporated into the transport description by means of a local-density approximation. Strong modifications of pi and delta production and absorption rates are found, but only small effects on pion observables.
The Hilbert class polynomial has as roots the j-invariants of elliptic curves whose endomorphism ring is a given imaginary quadratic order. It can be used to compute elliptic curves over finite fields with a prescribed number of points. Since its coefficients are typically rather large, there has been continued interest in finding alternative modular functions whose corresponding class polynomials are smaller. Best known are Weber's functions, that reduce the size by a factor of 72 for a positive density subset of imaginary quadratic discriminants. On the other hand, Br\"oker and Stevenhagen showed that no modular function will ever do better than a factor of 100.83. We introduce a generalization of class polynomials, with reduction factors that are not limited by the Br\"oker-Stevenhagen bound. We provide examples matching Weber's reduction factor. For an infinite family of discriminants, their reduction factors surpass those of all previously known modular functions by a factor at least 2.
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average transition probabilities are calculated. Stochastic density matrix method is developed, which is used for investigation of thermodinamical characteristics of the system, such as entropy and average energy.
In this paper, we examine the thermodynamic features of an exotic fluid known as modified cosmic Chaplygin gas in the context of homogeneous isotropic universe model. For this purpose, the behavior of physical parameters are discussed that help to analyze nature of the universe. Using specific heat formalism, the validity of third law of thermodynamics is checked. Furthermore, with the help of thermodynamic entities, the thermal equation of state is also discussed. The thermodynamic stability is explored by means of adiabatic, specific heat and isothermal conditions from classical thermodynamics. It is concluded that the considered fluid configuration is thermodynamically stable and expands adiabatically for an appropriate choice of parameters.
This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups.
When $A$ and $B$ are subsets of the integers in $[1,X]$ and $[1,Y]$ respectively, with $|A| \geq \alpha X$ and $|B| \geq \beta X$, we show that the number of rational numbers expressible as $a/b$ with $(a,b)$ in $A \times B$ is $\gg (\alpha \beta)^{1+\epsilon}XY$ for any $\epsilon > 0$, where the implied constant depends on $\epsilon$ alone. We then construct examples that show that this bound cannot in general be improved to $\gg \alpha \beta XY$. We also resolve the natural generalisation of our problem to arbitrary subsets $C$ of the integer points in $[1,X] \times [1,Y]$. Finally, we apply our results to answer a question of S\'ark\"ozy concerning the differences of consecutive terms of the product sequence of a given integer sequence.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
High resolution data in the region of the line Halpha have been obtained at the time of the light maximum and after it of the 2006 optical outburst of the symbiotic binary Z And. A blue-shifted absorption component indicating outflow velocity of about 1400 km/s as well as additional emission components with similar velocities, situated on the two sides of the main peak of the line were observed during that time. It is suggested that all of them are spectral signature of bipolar outflow, observed for the first time in the optical spectrum of this binary. The emission measure and the mass of the nebular part of the streams were estimated approximately.
In this letter, we discuss a new method to probe the redshift evolution of the gas depletion factor, i.e. the ratio by which the gas mass fraction of galaxy clusters is depleted with respect to the universal mean of baryon fraction. The dataset we use for this purpose consists of 40 gas mass fraction measurements measured at $r_{2500}$ using Chandra X-ray observations, strong gravitational lensing sub-samples obtained from SLOAN Lens ACS + BOSS Emission-line Lens Survey (BELLS) + Strong Legacy Survey SL2S + SLACS. For our analysis, the validity of cosmic distance duality relation is assumed. We find a mildly decreasing trend for the gas depletion factor as a function of redshift at about 2.7$\sigma$. This is the first result in literature which does not find a constant gas depletion factor as a function of redshift using gas mass fraction measurements at $r_{2500}$.
Superconducting qubits are hampered by flux noise produced by surface spins from a variety of microscopic sources. Recent experiments indicated that hydrogen (H) atoms may be one of those sources. Using density functional theory calculations, we report that H atoms either embedded in, or adsorbed on, an a-Al2O3(0001) surface have sizeable spin moments ranging from 0.81 to 0.87 uB with energy barriers for spin reorientation as low as ~10 mK. Furthermore, H adatoms on the surface attract gas molecules such as O2, producing new spin sources. We propose coating the surface with graphene to eliminate H-induced surface spins and to protect the surface from other adsorbates.
Using both a recent calculation by Bruch of the damping of the motion of a monolayer nitrogen film oscillating harmonically on a metallic surface due to Ohm's law heating and a Thomas-Fermi approximation treatment of the Ohm's law heating mechanism, which accounts for the nonzero thickness of the surface region of a metal, it is argued that this mechanism for friction is able to account for recent measurements of the drop in the friction for anitrogen film sliding over a lead substrate as it goes below its superconducting transition temperature. Bruch's calculation is also made more transparent by re-doing the calculation for a film sliding at constant speed, instead of oscillating. Using this treatment, it is easily shown that Bruch's calculation is equivalent to integrating Boyer's solution of the problem of a charge sliding over a metallic surface over the charge density of the monolayer nitrogen film.