ShantanuT01/DACTYL-Pretraining huggingface dataset:
Thermodynamic and magnetic properties of Ising models defined on the triangular Apollonian network are investigated. This and other similar networks are inspired by the problem of covering an Euclidian domain with circles of maximal radii. Maps for the thermodynamic functions in two subsequent generations of the construction of the network are obtained by formulating the problem in terms of transfer matrices. Numerical iteration of this set of maps leads to exact values for the thermodynamic properties of the model. Different choices for the coupling constants between only nearest neighbors along the lattice are taken into account. For both ferromagnetic and anti-ferromagnetic constants, long range magnetic ordering is obtained. With exception of a size dependent effective critical behavior of the correlation length, no evidence of asymptotic criticality was detected.
We examine the possibility of achieving quintessential inflation, where the same field serves as both inflaton and quintessence, in the context of a five-dimensional braneworld. Braneworld cosmology provides an appropriate environment as it permits inflation with much steeper potentials than the conventional scenario, which is favourable to a late-time quintessence. We explore a wide space of models, together with contemporary observational data, to determine in which contexts such a picture is possible. We find that such a scenario, although attractive, is in fact impossible to achieve for the potentials studied due to the restrictiveness of current data.
The formation of tidal dwarf galaxies (TDGs) is triggered by the encounters of already existing galaxies. Their existence is predicted from numerical calculations of encountering galaxies and is also well documented with observations. The numerical calculations on the formation of TDGs furthermore predict that TDGs cannot contain significant amounts of non-baryonic dark matter. In this paper, the first exhaustive sample of TDG-candidates from observations and numerical calculations is gathered from the literature. These stellar systems are gas-rich at the present, but they will probably evolve into gas-poor objects that are indistinguishable from old dwarf elliptical galaxies (dEs) based on their masses and radii. Indeed, known gas-poor TDGs appear as normal dEs. According to the currently prevailing cosmological paradigm, there should also be a population of primordial galaxies that formed within haloes of dark matter in the same mass range. Due to their different composition and origin, it would be expected that objects belonging to that population would have a different structure than TDGs and would thus be distinguishable from them, but such a population cannot be identified from their masses and radii. Moreover, long-lived TDGs could indeed be numerous enough to account for all dEs in the Universe. Downsizing, i.e. that less massive galaxies tend to be younger, would then be a natural consequence of the nature of the dEs. If these claims can be kept up in the light of future observations, the presently prevailing understanding of galaxy formation would need to be revised.
We investigate Lawruk elliptic boundary-value problems for homogeneous differential equations in a two-sided refined Sobolev scale. These problems contain additional unknown functions in the boundary conditions of arbitrary orders. The scale consists of inner-product H\"ormander spaces whose orders of regularity are given by any real number and a function which varies slowly at infinity in the sense of Karamata. We establish theorems on the Fredholm property of the problems in the refined Sobolev scale and on local regularity and local a priori estimate (up to the boundary of the domain) of their generalized solutions. We find sufficient conditions under which components of these solutions are $l\geq0$ times continuously differentiable functions.
The discoveries and open questions in neutrino physics, as reported at Neutrino 2002 and more recently, are reviewed from a theoretical perspective.
We study nonnegative solutions of the Cauchy problem $$ \begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0&\text{in } \mathbb{R}\times \{0\}, \end{cases} $$ where $u_0$ is a Radon measure and $\varphi:[0,\infty)\mapsto \mathbb{R}$ is a globally Lipschitz continuous function. We construct suitably defined entropy solutions in the space of Radon measures. Under some additional conditions on $\varphi$, we prove their uniqueness if the singular part of $u_0$ is a finite superposition of Dirac masses. In terms of the behaviour of $\varphi$ at infinity we give criteria to distinguish two cases: either all solutions are function-valued for positive times (an instantaneous regularizing effect), or the singular parts of certain solutions persist until some positive {\em waiting time} (in the linear case $\varphi(u)=u$ this happens for all times). In the latter case we describe the evolution of the singular parts.
Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.
A measure of cluster size heterogeneity ($H$), introduced by Lee et al [Phys. Rev. E {\bf 84}, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of $H$ to these clusters and, moreover, present new results for the geometric domains for both $d=2$ and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transition. An alternative interpretation for the scaling of $H$ that does not introduce a new exponent is also proposed.
In this paper we prove that every set $A\subset\mathbb{Z}$ satisfying the inequality $\sum_{x}\min(1_A*1_A(x),t)\le(2+\delta)t|A|$ for $t$ and $\delta$ in suitable ranges, then $A$ must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset $A\subset\mathbb{N}$ satisfies $|\mathbb{N}\setminus(A+A)|\ge k$; specifically we show that $\mathbb{P}(|\mathbb{N}\setminus(A+A)|\ge k)=\Theta(2^{-k/2})$.
We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their lightcurves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fit with this model, and the derived characteristic timescales ($t_c$) are in the range of $33\sim 264$ seconds. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gamma-rays, we estimate the Lorentz factors of the flares ($\Gamma_{\rm X}$). We obtain $\Gamma_{\rm X}=17\sim 87$ with a median value of $52$, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived $t_c$ and $\Gamma_{\rm X}$, we constrain the radiating regions of 13 X-ray flares, yielding $R_{\rm X}=(0.2\sim 1.1)\times 10^{16}$ cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in literatures, i.e., $\Gamma\propto [t_{p}/(1+z)]^{-0.69\pm 0.06}$. These results may shed lights on the long term evolution of GRB central engines.
We have performed angle resolved photoemission spectroscopy (ARPES) experiments on the surface states of SrTiO$_3$(001) using linearly and circularly polarized light to investigate the subband structures of out-of-plane $d_{xz/yz}$ orbitals and chiral orbital angular momentum (OAM). The data taken in the first Brillouin zone reveal new subbands for $d_{xz/yz}$ orbitals with Fermi wave vectors of 0.25 and 0.45 $\mathrm{\AA}^{-1}$ in addition to the previously reported ones. As a result, there are at least two subbands for all the Ti 3d t$_{2g}$ orbitals. Our circular dichroism ARPES data is suggestive of a chiral OAM structure in the surface states and may provide clues to the origin of the linear Rashba-like surface band splitting.
We address the problem of the percolative phase separation in polycrystalline samples of Pr$_{0.5-\delta}$Ca$_{0.2+\delta}$Sr$_{0.3}$MnO$_3$ for $-0.04\leq \delta \leq 0.04$ (hole doping $n$ between 0.46 and 0.54). We perform measurements of X-ray diffraction, dc magnetization, ESR, and electrical resistivity. These samples show at $T_C$ a paramagnetic (PM) to ferromagnetic (FM) transition, however, we found that for $n>0.50$ there is a coexistence of both of these phases below $T_C$. On lowering $T$ below the charge-ordering (CO) temperature $T_{CO}$ all the samples exhibit a coexistence between the FM metallic and CO (antiferromagnetic) phases. In the whole $T$ range the FM phase fraction ($X$) decreases with increasing $n$. Furthermore, we show that only for $n\leq 0.50$ the metallic fraction is above the critical percolation threshold $X_C\simeq 15.5%$. As a consequence, these samples show very different magnetoresistance properties. In addition, for $n\leq 0.50$ we observe a percolative metal-insulator transition at $T_{MI}$, and for $T_{MI}<T<T_{CO}$ the insulating-like behavior generated by the enlargement of $X$ with increasing $T$ is well described by the percolation law $\rho ^{-1}=\sigma \sim (X-X_C)^t$, where $t$ is a critical exponent. On the basis of the values obtained for this exponent we discuss different possible percolation mechanisms, and suggest that a more deep understanding of geometric and dimensionality effects is needed in phase separated manganites. We present a complete $T$ vs $n$ phase diagram showing the magnetic and electric properties of the studied compound around half doping.
Microwave induced photoconductivity of a two-dimensional electron gas (2DEG) in selectively-doped GaAs/AlAs heterostructures has been studied using the Corbino geometry with capacitive contacts at a temperature T=1.6K and magnetic field B up to 0.5 T. Zero-conductance states have been observed in the samples under study subject to microwave radiation, similarly to the samples with ohmic contacts. It has been shown that ohmic contacts do not play a significant role for observation of zero-conductance states induced by microwave radiation
Let $\bf f$ be a primitive Hilbert cusp form of weight $k$ and level $\mathfrak{n}$ with Fourier coefficients $c_{\bf f}(\mathfrak{m})$. We prove a non-trivial upper bound for almost all Fourier coefficients $c_{\bf f}(\mathfrak{m})$ of $\bf f$. This generalizes the bounds obtained by Luca, Radziwi\l{}\l{} and Shparlinski. We also prove the existence of infinitely many integral ideals $\mathfrak{m}$ for which the Fourier coefficients $c_{\bf f}(\mathfrak{m})$ have the improved upper bound and further we obtain a refinement of these integral ideals in terms of prime powers. In particular, this enable us to deduce the bound for Fourier coefficients of elliptic cusp forms beyond the `typical size'. Moreover, we prove further improvements of the bound under the assumption of Littlewood's conjecture. Finally, We study a lower bound for the Fourier coefficients at prime powers provided the corresponding Hecke eigen angle is badly approximable.
Star formation occurs via fragmentation of molecular clouds, which means that the majority of stars born are a members of binaries. There is growing evidence that planets might form in circumprimary disks of medium-separation binaries. The tidal forces caused by the secondary generally act to distort the originally circular disk to an eccentric one. To infer the disk eccentricity from high-res NIR spectroscopy, we calculate the fundamental band emission lines of the CO molecule emerging from the atmosphere of the disk. We model circumprimary disk evolution under the gravitational perturbation of the orbiting secondary using a 2D grid-based hydrodynamical code, assuming alpha-type viscosity. The hydrodynamical results are combined with our spectral code based on the double-layer disk model to calculate the CO molecular line profiles. We find that the orbital velocity distribution of the gas parcels differs significantly from the circular Keplerian fashion, thus the line profiles are asymmetric in shape. The magnitude of asymmetry is insensitive to the binary mass ratio, the magnitude of viscosity, and the disk mass. In contrast, the disk eccentricity, thus the level of the line profile asymmetry, is influenced significantly by the binary eccentricity and the disk geometrical thickness. We demonstrate that the disk eccentricity profile in the planet-forming region can be determined by fitting the high-resolution CO line profile asymmetry using a simple 2D spectral model that accounts for the velocity distortions caused by the disk eccentricity. Thus, with our novel approach the disk eccentricity can be inferred with high-resolution near-IR spectroscopy prior to the era of high angular resolution optical or radio direct-imaging. By determining the disk eccentricity in medium-separation young binaries, we might be able to constrain the planet formation theories.
Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti numbers in the so-called `sparse' regime. Specifically, we consider a piecewise constant Gaussian field whose covariance function is positive and satisfies some local, boundedness, and decay rate conditions. We model its excursion set via a Cech complex. For Betti numbers of this complex, we then prove various limit theorems as the window size and the excursion level together grow to infinity. Our results include asymptotic mean and variance estimates, a vanishing to non-vanishing phase transition with a precise estimate of the transition threshold, and a weak law in the non-vanishing regime. We further obtain a Poisson approximation and a central limit theorem close to the transition threshold. Our proofs combine extreme value theory and combinatorial topology tools.
We show that there is an infinite number of U(1) symmetries like Peccei-Quinn symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets. Moreover, all of them are completely broken due to the model's scalars by themselves (notice that these scalars as known have been often used to break the gauge symmetry and generating the masses for the model's particles). There is no any residual Peccei-Quinn symmetry. Because of the minimal scalar content there are some quarks that are massless at tree-level, but they can get consistent mass contributions at one-loop due to this fact. Interestingly, axions as associated with the mentioned U(1)s breaking (including Majoron due to lepton-charge breaking) are all gauged away because they are also the Goldstone bosons responsible for the gauge symmetry breaking as usual.
We consider the following singularly perturbed elliptic problem $$ \varepsilon^2\triangle\tilde{u}-\tilde{u}+\tilde{u}^p=0, \ \tilde{u}>0\quad \mbox{in} \ \Omega,\ \ \ \frac{\partial\tilde{u}}{\partial \mathbf{n}}=0 \quad \mbox{on}\ \partial\Omega, $$ where $\Omega$ is a bounded domain in $\mathbb{R}^3$ with smooth boundary, $\varepsilon$ is a small parameter, $\mathbf{n}$ denotes the inward normal of $ \partial\Omega$ and the exponent $p>1$. Let $\Gamma$ be a hypersurface intersecting $\partial\Omega$ in the right angle along its boundary $\partial\Gamma$ and satisfying a {\em non-degenerate condition}. We establish the existence of a solution $u_\varepsilon$ concentrating along a surface $\tilde{\Gamma}$ close to $\Gamma$, exponentially small in $\varepsilon$ at any positive distance from the surface $\tilde{\Gamma}$, provided $\varepsilon$ is small and away from certain {\em critical numbers}. The concentrating surface $\tilde{\Gamma}$ will collapse to $\Gamma$ as $\varepsilon\rightarrow 0$.
We prove the existence and uniqueness of a strong solution for an SDE on a semi-axis with singularities at the point 0. The result obtained yields, for example, the strong uniqueness of non-negative solutions to SDEs governing Bessel processes.
We present a spectroscopic study of excitation dynamics in self assembled CdTe/ZnTe quantum dots. Insight into details of kinetics is obtained from the time resolved micro-photoluminescence, single photon correlation and subpicosecond excitation correlation measurements done on single quantum dots. It is shown that the pulsed excitation in energy above the energy gap of the barrier material results in separate capture of electrons and holes. The capture of carriers of different charge take place at different delay from excitation.
Fast radio bursts are radio transients observed mainly around 1.5 GHz. Their peak frequency decreases at a rate of 100 ~ 500 MHz/s and some of them have a broader pulse with an exponentially decaying tail. Common assumptions for fast radio bursts include a dispersion effect resulting in the peak frequency drifting and a scattering effect resulting in pulse broadening. These assumptions attribute the abnormally large dispersion measure and scattering measure to the environmental medium of the host galaxy. Here we show that the radiation of fast radio bursts can be explained as an undulator radiation and the large dispersion measure can be due to a motion effect mainly from the rotation of the source which is probably variable stars. In our scenario, the pulse broadening is near-field effects and the pulse itself represents a Fresnel diffraction pattern sweeping the observer. Our work is the first analysis of properties of fast radio bursts in the context of a special mechanism of the radiation instead of a special propagation environment of the radiation.
The electronic and transport properties of graphene modulated by magnetic barrier arrays are derived for finite temperature. Prominent conductance gaps, originating from quantum interference effects are found in the periodic array case. When a structural defect is inserted in the array, sharp defect modes of high conductance appear within the conductance gaps. These modes can be shifted by local doping in the defect region resulting into sensing of the chemical molecules that adhere on the graphene sheet. In general it is found that sensitivity is strongly dependent on temperature due to smoothing out of the defect-induced peaks and transport gaps. This temperature dependence, however, offers the added capability for sub-mK temperature sensing resolution, and thus an opportunity towards ultra-sensitive combined electrochemical-calorimetric sensing.
Non-thermal radio emission from cosmic ray electrons in the vicinity of merging galaxy clusters is an important tracer of cluster merger activity, and is the result of complex physical processes that involve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of cosmic ray electron acceleration that are then input into radio emission models. We have determined the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio observations to compare to observed galaxy clusters. We find a significant dependence of the observed morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding the interpretation of observed radio features in clusters. We also find that a given shock should not be characterized by a single Mach number. We find that the bulk of the radio emission comes from gas with T>5x10^7, \rho~10^(-28)-10^(-27) g/cm^3, with magnetic field strengths of 0.1-1.0 \mu G and shock Mach numbers of M~3-6. We present an analysis of the radio spectral index which suggests that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the polarization fraction and position angle of the simulated radio features, and compare to observations.
Chandra images of galaxy clusters have revealed a wealth of structure unseen by previous generations of low resolution X-ray observatories. In the cores of clusters, bright, irregular X-ray emission is now routinely seen within central dominant galaxies (CDGs) harboring powerful radio sources. The radio sources are interacting with and are often displacing the hot gas leaving cavities in their wakes. The cavities rise buoyantly, transporting up to 10E61 ergs of energy to the intracluster medium over the life of a cluster. The dynamically important magnetic fields observed in cooling flows may have originated from these cavities. The cooling rates found by Chandra and XMM-Newton are much smaller than previously reported, and they are more in line with the levels of cold gas and star formation seen in other bandpasses. I discuss the emerging correlation between extended H-alpha emission, star formation, and bright X-ray emission at locations where the cooling time of the keV gas approaches a few hundred million years. Data from a variety of disciplines suggest repeated, short duration bursts of cooling and star formation are occurring, possibly induced and regulated in some instances by the central radio source. Finally, I discuss the interesting possibility that radio sources quench cooling flows, while emphasizing the difficulties with some proposed scenarios.
We investigate the differentiability issue of the drift-diffusion equation with nonlocal L\'evy-type diffusion at either supercritical or critical type cases. Under the suitable conditions on the drift velocity and the forcing term in terms of the spatial H\"older regularity, we prove that the vanishing viscosity solution is differentiable with some H\"older continuous derivatives for any positive time.