ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we investigate the initial-boundary value problem to the heat conductive compressible Navier-Stokes equations. Local existence and uniqueness of strong solutions is established with any such initial data that the initial density $\rho_0$, velocity $u_0$, and temperature $\theta_0$ satisfy $\rho_0\in W^{1,q}$, with $q\in(3,6)$, $u_0\in H^1$, and $\sqrt{\rho_0}\theta_0\in L^2$. The initial density is assumed to be only nonnegative and thus the initial vacuum is allowed. In addition to the necessary regularity assumptions, we do not require any initial compatibility conditions such as those proposed in (Y. Cho and H. Kim, \emph{Existence results for viscous polytropic fluids with vacuum}, J. Differential Equations {\bf 228} (2006), no.~2, 377--411.), which although are widely used in many previous works but put some inconvenient constraints on the initial data. Due to the weaker regularities of the initial data and the absence of the initial compatibility conditions, leading to weaker regularities of the solutions compared with those in the previous works, the uniqueness of solutions obtained in the current paper does not follow from the arguments used in the existing literatures. Our proof of the uniqueness of solutions is based on the following new idea of two-stages argument: (i) showing that the difference of two solutions (or part of their components) with the same initial data is controlled by some power function of the time variable; (ii) carrying out some singular-in-time weighted energy differential inequalities fulfilling the structure of the Gr\"onwall inequality. The existence is established in the Euler coordinates, while the uniqueness is proved in the Lagrangian coordinates first and then transformed back to the Euler coordinates.
We apply the Lanczos method to a 2-leg ladder with mixed spins of magnitudes $(S_1,S_2)=(1,1/2)$ located at alternating positions along the ladder. The effect of dimerization $\gamma$ is also considered according to two different patterns. A Spin Wave Theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low energy excitations of the model. We compute the ground state energies, Ferro- and AF-excitation gaps, magnetizations and correlation functions as a function of $J'$ and $\gamma$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the Spin-Peierls instability and find that it is conditional for any value of $ J' \in (0, 2)$ and both dimerization patterns.
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class solutions which are formally asymptotically in $L^2(\mathbb{R})$. A precise rate of convergence is also obtained assuming more regularity.
A positive integer $A$ is called a congruent number if $A$ is the area of a right-angled triangle with three rational sides. Equivalently, $A$ is a congruent number if and only if the congruent number curve $y^2=x^3-A^2x$ has a rational point $(x,y)\in\mathbb Q^2$ with $y\neq 0$. Using a theorem of Fermat, we give an elementary proof for the fact that congruent number curves do not contain rational points of finite order.
In this paper we present the equations of the evolution of the universe in $D$ spatial dimensions, as a generalization of the work of Lima \citep{lima}. We discuss the Friedmann-Robertson-Walker cosmological equations in $D$ spatial dimensions for a simple fluid with equation of state $p=\omega_{D}\rho$. It is possible to reduce the multidimensional equations to the equation of a point particle system subject to a linear force. This force can be expressed as an oscillator equation, anti-oscillator or a free particle equation, depending on the $k$ parameter of the spatial curvature. An interesting result is the independence on the dimension $D$ in a de Sitter evolution. We also stress the generality of this procedure with a cosmological $\Lambda$ term. A more interesting result is that the reduction of the dimensionality leads naturally to an accelerated expansion of the scale factor in the plane case.
H\alpha\ equivalent widths and UBV magnitudes are calculated for Be star disk models that grow in size and/or density with time. We show that these simple models are consistent with the known Be star classes of positive and inverse correlations between long-term variations in H\alpha\ and V magnitude as identified by Harmanec. We support the conclusion of Harmanec that the distinction is controlled by the inclination of the disk to the line of sight. We demonstrate that the strength of these correlations, particularly those of an inverse correlation where the system becomes fainter as the H\alpha\ emission strength grows, is strongly influenced by the scale height of the inner Be star disk and the extent of the gravitational darkening of the central B star due to rapid rotation. This dependence may allow coordinated spectroscopic and photometric observations to better constrain these poorly known Be star parameters.
Studies of star formation rely heavily on observations in the near-infrared, but they typically need information from other wavelengths for interpretation. We show that we can infer distances and estimate the membership of young stellar objects for young clusters independently using (ground-based) near-infrared, $J$, $H,$ and $K_S$ broadband data alone. We also show that we can estimate a lower limit for the fraction of sources with $2.2~\mu$m excess emission with a sensitivity comparable to that of mid-infrared space data, but with better resolution and fewer biases. Finally, we show that the typical methods for inferring masses from these data may produce substantially unreliable results. This method is applied to the young, massive cluster RCW 38, for which we estimate a distance of 1.5 kpc and a $K_S$-band excess fraction larger than 60\%.
An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams $E_6, E_7$, $E_8$. These curves are non-hyperelliptic of genus 3 or 4. We prove that a positive proportion of each family consists of curves with integral points everywhere locally but no integral points globally.
We theoretically study dynamic properties of thin ferromagnetic films in contact with normal metals. Moving magnetizations cause a flow of spins into adjacent conductors, which relax by spin flip, scatter back into the ferromagnet, or are absorbed by another ferromagnet. Relaxation of spins outside the moving magnetization enhances the overall damping of the magnetization dynamics in accordance with the Gilbert phenomenology. Transfer of spins between different ferromagnets by these nonequilibrium spin currents leads to a long-ranged dynamic exchange interaction and novel collective excitation modes. Our predictions agree well with recent ferromagnetic-resonance experiments on ultrathin magnetic films.
Recent observations demonstrate that dwarf elliptical (dE) galaxies in clusters, despite their faintness, are likely a critical galaxy type for understanding the processes behind galaxy formation. Dwarf ellipticals are the most common galaxy type, and are particularly abundant in rich galaxy clusters. The dwarf to giant ratio is in fact highest in rich clusters of galaxies, suggesting that cluster dEs do not form in groups that later merge to form clusters. Dwarf ellipticals are potentially the only galaxy type whose formation is sensitive to global, rather than local, environment. The dominant idea for explaining the formation of these systems, through Cold Dark Matter models, is that dEs form early and within their present environments. Recent results suggest that some dwarfs appear in clusters after the bulk of massive galaxies form, a scenario not predicted in standard hierarchical structure formation models. Many dEs have younger and more metal rich stellar populations than dwarfs in lower density environments, suggesting processes induced by rich clusters play an important role in dE formation. Several general galaxy cluster observations, including steep luminosity functions, and the origin of intracluster light, are natural outcomes of this delayed formation.
The paper contains at the end a proof of the conjecture of Gross - Kuz'min, for CM extensions of Q. The main topic of the paper is the investigation of the growth of order and ranks at finite levels of some Lambda modules (p-parts of ideal class groups).
Radio-frequency compressed ultrafast electron diffraction has been used to probe the coherent and incoherent coupling of impulsive electronic excitation at 1.55 eV (800 nm) to optical and acoustic phonon modes directly from the perspective of the lattice degrees of freedom. A bi-exponential suppression of diffracted intensity due to relaxation of the electronic system into incoherent phonons is observed, with the 250 fs fast contribution dominated by coupling to the $E_{2g2}$ optical phonon mode at the $\Gamma$-point ($\Gamma-E_{2g2}$) and $A_1^{'}$ optical phonon mode at the $K$-point ($K-A_1^{'}$). Both modes have Kohn anomalies at these points in the Brillouin zone. The result is a unique non-equilibrium state with the electron subsystem in thermal equilibrium with only a very small subset of the lattice degrees of freedom within 500 fs following photoexcitation. This state relaxes through further electron-phonon and phonon-phonon pathways on the 6 ps timescale. In addition, electronic excitation leads to both in-plane and out-of-plane coherent lattice responses in graphite whose character we are able to fully determine based on spot positions and intensity modulations in the femtosecond electron diffraction data. The in-plane motion is specifically a $\Gamma$-point shearing mode of the graphene planes with an amplitude of approximately 0.06 pm and the out-of-plane motion an acoustic breathing mode response of the film.
In this paper we consider the initial value problem of the Benjamin equation $$ \partial_{t}u+\nu \H(\partial^2_xu)   +\mu\partial_{x}^{3}u+\partial_xu^2=0, $$ where $u:\R\times [0,T]\mapsto \R$, and the constants $\nu,\mu\in \R,\mu\neq0$. We use the I-method to show that it is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>-3/4$. Moreover, we use some argument to obtain a good estimative for the lifetime of the local solution, and employ some multiplier decomposition argument to construct the almost conserved quantities.
We study the finite temperature phase diagram of the Heisenberg-Kitaev model on a three dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte-Carlo simulations, we investigate quantum and thermal order-by-disorder, as well as the magnetic ordering temperature. We find the parameter regime where quantum and thermal fluctuations favor different magnetic orders, which leads to an additional finite temperature phase transition within the ordered phase. This transition, however, occurs at a relatively low temperature and the entropic effects may dominate most of the finite temperature region below the ordering temperature. In addition, we explore the magnetization process in the presence of a magnetic field and discover spin-flop transitions which are sensitive to the applied-field direction. We discuss implications of our results for future experiments on a hyperhoneycomb lattice system such as the recently discovered \beta-Li2IrO3.
Pre-main sequence (PMS) stars of mass $\gtrsim0.35\,{\rm M}_\odot$ transition from hosting fully convective interiors to configurations with a radiative core and outer convective envelope during their gravitational contraction. This stellar structure change influences the external magnetic field topology and, as we demonstrate herein, affects the coronal X-ray emission as a stellar analog of the solar tachocline develops. We have combined archival X-ray, spectroscopic, and photometric data for $\sim$1000 PMS stars from five of the best studied star forming regions; the ONC, NGC 2264, IC 348, NGC 2362, and NGC 6530. Using a modern, PMS calibrated, spectral type-to-effective temperature and intrinsic colour scale, we deredden the photometry using colours appropriate for each spectral type, and determine the stellar mass, age, and internal structure consistently for the entire sample. We find that PMS stars on Henyey tracks have, on average, lower fractional X-ray luminosities ($L_{\rm X}/L_\ast$) than those on Hayashi tracks, where this effect is driven by changes in $L_{\rm X}$. X-ray emission decays faster with age for higher mass PMS stars. There is a strong correlation between $L_\ast$ and $L_{\rm X}$ for Hayashi track stars but no correlation for Henyey track stars. There is no correlation between $L_{\rm X}$ and radiative core mass or radius. However, the longer stars have spent with radiative cores, the less X-ray luminous they become. The decay of coronal X-ray emission from young early K to late G-type PMS stars, the progenitors of main sequence A-type stars, is consistent with the dearth of X-ray detections of the latter.
Using an effective Hamiltonian parametrized from first principles, Monte Carlo simulations are performed in order to study the piezoelectric response of BaTiO3 in the ferroelectric tetragonal phase as a function of temperature. The effect of an electric field on the phase behavior is also illustrated by a simulation of the transformation of a rhombohedral domain into a tetragonal one under a strong field.
We find remarkable agreement with the observed excitations of hadrons with a simple three parameter mass relation of the SU(3) subgroup of the underlying U(15/30) graded Lie group. The baryons are the appropriate supersymmetric partners of the mesons. An interesting feature, which is a focus of current interest, is that the baryons and isobars show parity doubling. Significantly, the ground state baryons and mesons have no place in the fit, so that the parity doubling is indicated only when excitation energy is available. This has correspondence with the parity doubling seen in recent lattice calculations, when thermal excitation is present. The agreement with experiment is comparable to the semi-relativistic quark model which fits with many force parameters and where the observed parity doubling is accidental. The gross splitting of the levels is the same for the strange and the non-strange sectors, suggesting flavour independence.
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion and magnetic Gr\"uneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven by geometrical frustration. We also discovered a spin-flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin-liquid like state.
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) contains a singlet-like pseudoscalar Higgs boson in addition to the doublet-like pseudoscalar of the Minimal Supersymmetric Standard Model. This new pseudoscalar can have a very low mass without violating the LEP exclusion constraints and it can potentially provide a hallmark signature of non-minimal supersymmetry at the LHC. In this analysis we revisit the light pseudoscalar in the NMSSM with partial universality at some high unification scale. We delineate the regions of the model's parameter space that are consistent with the up-to-date theoretical and experimental constraints, from both Higgs boson searches and elsewhere (most notably $b$-physics), and examine to what extent they can be probed by the LHC. To this end we review the most important production channels of such a Higgs state and assess the scope of its observation at the forthcoming Run-2 of the LHC. We conclude that the $b\bar{b}$-associated production of the pseudoscalar, which has been emphasised in previous studies, does not carry much promise anymore, given the measured mass of the Higgs boson at the LHC. However, the decays of one of the heavier scalar Higgsbosons of the NMSSM can potentially lead to the discovery of its light pseudoscalar. Especially promising are the decays of one or both of the two lightest scalar states into a pseudoscalar pair and of the heaviest scalar into a pseudoscalar and a $Z$ boson. Since the latter channel has not been explored in detail in the literature so far, we provide details of some benchmark points which can be probed for establishing its signature.
For a rational prime p, let k be a perfect field of characteristic p, K be a finite totally ramified extension of Frac(W(k)) of degree e and r be a non-negative integer satisfying r<p-1. In this article, we prove the upper numbering ramification group G^(j) for j>u(K,r,n) acts trivially on the p^n-torsion semi-stable G_K-representations with the Hodge-Tate weights in {0,...,r}, where u(K,0,n)=0, u(K,1,n)=1+e(n+1/(p-1)) and u(K,r,n)=1-p^{-n}+e(n+r/(p-1)) for r>1.
The contradiction between the stationary aproach to the density profile and the avalanche character of the metastable phase consumption is investigated. The exact solution for the metastable phase profile is obtained. The reconsidered value for the special parameter responsible for the hierarchy in the structure of the density profile around the droplet is presented.
Observations of the optical afterglow of GRB 041006 with the Kiso Observatory 1.05 m Schmidt telescope, the Lulin Observatory 1.0 m telescope and the Xinglong Observatory 0.6 m telescope. Three-bands (B, V and R) of photometric data points were obtained on 2004 October 6, 0.025-0.329 days after the burst. These very early multi band light curves imply the existence of a color dependent plateau phase. The B-band light curve shows a clear plateau at around 0.03 days after the burst. The R band light curve shows the hint of a plateau, or a possible slope change, at around 0.1 days after the burst. The overall behavior of these multi-band light curves may be interpreted in terms of the sum of two separate components, one showing a monotonic decay the other exhibiting a rising and a falling phase, as described by the standard afterglow model.
Recent observational and theoretical arguments suggest that magnetic OB stars may suffer more mixing than their non magnetic analogs. We present the results of an NLTE abundance study revealing a lack of CN-cycled material at the surface of two magnetic stars discovered by the MiMeS project (NGC2244 #201 and HD 57682). The existence of a strong magnetic field is therefore not a sufficient condition for deep mixing in main-sequence OB stars.
Since the launch of the Fermi Gamma-Ray Space Telescope, several hundred gamma-ray pulsars have been discovered, some being radio-loud and some radio-quiet with time-aligned radio and gamma-ray light curves. In the second Fermi Pulsar Catalogue, 117 new gamma-ray pulsars have been reported based on three years of data collected by the Large Area Telescope on the Fermi satellite, providing a wealth of information such as the peak separation~$\Delta$ of the gamma-ray pulsations and the radio lag~$\delta$ between the gamma-ray and radio pulses. We selected several radio-loud millisecond gamma-ray pulsars with period~$P$ in the range 2-6~ms and showing a double peak in their gamma-ray profiles. We attempted to constrain the geometry of their magnetosphere, namely the magnetic axis and line-of-sight inclination angles for each of these systems. We applied a force-free dipole magnetosphere from the stellar surface up to the striped wind region -- well outside the light cylinder -- to fit the observed pulse profiles in gamma-rays, consistently with their phase alignment with the radio profile. In deciding whether a fitted curve is reasonable or not, we employed a least-square method to compare the observed gamma-ray intensity with that found from our model, emphasising the amplitude of the gamma-ray peaks, their separation, and the phase lag between radio and gamma-ray peaks. We obtained the best fits and reasonable parameters in agreement with observations for ten millisecond pulsars. Eventually, we constrained the geometry of each pulsar described by the magnetic inclination~$\alpha$ and the light-of-sight inclination~$\zeta$. We found that both angles are larger than approximately~$45^{\rm o}$.
This essay elucidates recent achievements of the "nongravitating vacuum energy" (NGVE) theory" which has the feature that a shift of the Lagrangian density by a constant does not affect dynamics. In the first order formalism, a constraint appears that enforces the vanishing of the cosmological constant \Lambda. Standard dynamics of gauge unified theories (including fermions) and their SSB appear if a four index field strength condensate is present. At a vacuum state there is exact balance to zero of the gauge fields condensate and the original scalar fields potential. As a result it is possible to combine the solution of the \Lambda problem with inflation and transition to a \Lambda =0 phase without fine tuning after a reheating period. The model opens new possibilities for a solution of the hierarchy problem.
We have compared the morphological characteristics of the 891 galaxies in the Extended 12-micron Sample (E12GS), and assessed the effect of the 12-micron selection criterion on galaxy properties. The normal spirals in the E12GS have the same axial ratios, morphological types, and bar and ring fractions as other normal spirals. The HII/starburst galaxies have a higher incidence of bars, and more than twice the normal rate of "peculiar" morphologies, both of which are attributable to relatively recent disturbances. The galaxies with active nuclei (AGNs: Seyferts and LINERs) have the same incidence of bars as normal spirals, but show rings significantly more often than normal galaxies or starbursts. The LINERs have elevated rates of inner rings, while the Seyferts have outer ring fractions several times those in normal galaxies. The different formation times of bars and rings suggest an interpretation of these differences. Bars form relatively quickly, and indicate that material is recently being transported (by redistribution of angular momentum) to the center of the galaxy, where it is likely to trigger a short (e.g., $\lesssim 10^8$ yrs) burst of star formation. Outer rings may result from similar disturbances, but require much more time to form, while inner rings form in a shorter time, more comparable to bars. Thus it may be that after an interaction or instability triggers an infall of gas, the galaxy in the earliest stage is likely to show enhanced star formation in its center, while later it is more likely to show LINER activity, and still later likely to be a Seyfert.