ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a Cahn-Hilliard-Hele-Shaw (or Cahn-Hilliard-Darcy) system for an incompressible mixture of two fluids. The relative concentration difference $\varphi$ is governed by a convective nonlocal Cahn-Hilliard equation with degenerate mobility and logarithmic potential. The volume averaged fluid velocity $\mathbf{u}$ obeys a Darcy's law depending on the so-called Korteweg force $\mu\nabla \varphi$, where $\mu$ is the nonlocal chemical potential. In addition, the kinematic viscosity $\eta$ may depend on $\varphi$. We establish first the existence of a global weak solution which satisfies the energy identity. Then we prove the existence of a strong solution. Further regularity results on the pressure and on $\mathbf{u}$ are also obtained. Weak-strong uniqueness is demonstrated in the two dimensional case. In the three-dimensional case, uniqueness of weak solutions holds if $\eta$ is constant. Otherwise, weak-strong uniqueness is shown by assuming that the pressure of the strong solution is $\alpha$-H\"{o}lder continuous in space for $\alpha\in (1/5,1)$.
The Bayesian neural network (BNN) has been applied to evaluate and predict the nuclear data. However, how to provide physics guides in BNN is a key but an open question. In this work, the case study on giant dipole resonance (GDR) energy is presented to illustrate the effectiveness and maneuverability of the method to provide physics guides in BNN from input layer. The Spearman's correlation coefficients are applied to assess the statistical dependence between nuclear properties in the ground state and the GDR energies. Then the optimal ground-state properties are employed as the input layer in the BNN for evaluating and predicting the GDR energies. Those selected ground-state properties actively contributes to reduce the predicted errors and avoid the risk of the non-physics divergence. This work gives a demonstration to find effects of the GDR energy by using the BNN without the physics motivated model, which may be helpful for discovering physics effects from the complex nuclear data.
Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.
In this paper, we investigate the invasion percolation (IP) in imperfect support in which the configuration of imperfections is considered to be correlated. Three lattice models were engaged to realize this pattern: site percolation, Ising model and random Coulomb potential (RCP). The first two models are short range interaction (SRI), whereas the last one includes coulomb like interactions which is pretty long range (long-range interactions, LRI). By examining various dynamical observables we show that the critical exponents of SRI IP are robust against the control parameters (temperature in the Ising model and occupation probability in site percolation), whereas its properties in the LRI (RCP) supports are completely different from the normal IP (i.e. on the regular lattice). Especially the fractal dimension of the external frontier of the largest hole converges to $1.099\pm 0.008$ for RCP IP, whereas it is nearly $\frac{4}{3}$ for SRI IP being compatible with normal IP. Additionally a novel dynamical crossover is seen in the RCP IP according to which the time dependence of all of the observables is divided to three parts: the power-law (small times), the logarithmic (mid time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The observables become nearly constant in the thermodynamic limit for the long time, showing that it is a stationary phase.
Kondo insulating materials lie outside the usual dichotomy of weakly versus correlated - band versus Mott - insulators. They are metallic at high temperatures but resemble band insulators at low temperatures because of the opening of an interaction induced band gap. The first discovered Kondo insulator (KI) SmB$_6$ has been predicted to form a topological KI (TKI) which mimics a topological insulator at low temperatures. However, since its discovery thermodynamic and transport anomalies have been observed that have defied a theoretical explanation. Enigmatic signatures of collective modes inside the charge gap are seen in specific heat, thermal transport and quantum oscillation experiments in strong magnetic fields. Here, we show that TKIs are susceptible to the formation of excitons and magneto-excitons. These charge neutral composite particles can account for long-standing anomalies in SmB$_6$ which is crucial for the identification of bulk topological signatures.
We report a detection of an absorption line at ~44.8 {\AA} in a > 500 ks Chandra HRC-S/LETG X-ray grating spectrum of the blazar H 2356-309. This line can be identified as intervening CV-K{\alpha} absorption, at z\approx0.112, produced by a warm (log T = 5.1 K) intergalactic absorber. The feature is significant at a 2.9{\sigma} level (accounting for the number of independent redshift trials). We estimate an equivalent hydrogen column density of log N_H=19.05 (Z/Zsun)^-1 cm^-2. Unlike other previously reported FUV/X-ray metal detections of warm-hot intergalactic medium (WHIM), this CV absorber lies in a region with locally low galaxy density, at ~2.2 Mpc from the closest galaxy at that redshift, and therefore is unlikely to be associated with an extended galactic halo. We instead tentatively identify this absorber with an intervening Warm-Hot Intergalactic Medium filament possibly permeating a large-scale, 30 Mpc extended, structure of galaxies whose redshift centroid, within a cylinder of 7.5 Mpc radius centered on the line of sight to H 2356-309, is marginally consistent (at a 1.8{\sigma} level) with the redshift of the absorber.
(ABRIDGED) We use high resolution (~0.1") F814W ACS images from the HST ACS Treasury survey of the Coma cluster at z~0.02 to study bars in massive disk galaxies (S0s), and in dwarf galaxies in the Coma core. Our study helps constrain the evolution of bars and disks in dense environments and provides a comparison point for studies in lower density environments and at higher redshifts. (1) We characterize the fraction and properties of bars in a sample of 32 bright (M_V <= -18, M_* > 10^9.5 M_sun) S0 galaxies, which dominate the population of massive disk galaxies in the Coma core. Measuring the S0 bar fraction must be handled carefully, as the results depend on the method used: the bar fraction for bright S0s in the Coma core is 50%+/-11%, 65%+/-11%, and 60%+/-11% for three methods of bar detection: strict ellipse fit criteria, relaxed ellipse fit criteria, and visual classification. (2) We compare the S0 bar fraction across different environments (Coma core, A901/902, Virgo). We find that the bar fraction among bright S0 galaxies does not show a statistically significant variation across environments spanning two orders of magnitude in galaxy number density (n~300-10,000 gal/Mpc^3). We speculate that the S0 bar fraction is not significantly enhanced in rich clusters because S0s in rich clusters are less prone to bar instabilities as they are dynamically hot and gas poor due to ram pressure stripping and accelerated star formation. In addition, high-speed encounters in rich clusters may be less effective than slow, strong encounters in inducing bars. (3) We analyze a sample of 333 faint (M_V > -18) dwarf galaxies in the Coma core. Using unsharp-masking, we find only 13 galaxies with bar and/or spiral structure. The paucity of disk structures in Coma dwarfs suggests that either disks are not common in these galaxies, or that any disks present are too hot to develop instabilities.
We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss possibility of condensation there.
We have studied the magnetic and transport behavior of doped La0.65 A0.35 Mn0.95Fe0.05 O3 (A= Ca, Sr, Pb, Ba) compounds. All the compositions show ferromagnetic/metal to paramagnetic/insulator transition except the Pb doped sample which is insulating and ferromagnetic in the entire temperature range. The simultaneous occurrence of ferromagnetism and insulating behavior in Pb doped compound is most likely due to the presence of FM clusters separated by Fe and Mn ions that are coupled AFM and hence prevent the current from crossing the inter-domain region. The magnetization and Tc are decreased by decreasing the Cation size on La site. We observed that (for a fixed Fe content of 5%) the transition temperature and magnetic moment at 77 K is a maximum for Sr doped sample and is decreasing if we increase or decrease the cation size from Sr size. The maximum value of Tc and magnetic moment for Sr based sample is most likely due to the closer ionic sizes of La and Sr as compared to the other dopants (Ca, Pb, Ba). The decrease in the transition temperature and magnetic moment is due to the deviation of Mn-O-Mn angle from 1800 caused by the size mismatch of the A site cations. This deviation leads to weakening of the FM double exchange (DE). We observed a spin freezing type effect in the Pb doped sample below 120 K in resistivity, AC susceptibility and in magnetization. This suggests that the AFM interactions introduced by the Fe are most effective in the Pb doped composition leading to increased competition between the FM and AFM interactions. This FM and AFM interaction generates some degree of frustration leading to the appearance of spin glass like phase whose typical magnetic behavior is studied for small ion when the metallic like behavior is lost.
The Landauer conductance of a two terminal device equals to the number of open modes in the weak scattering limit. What is the corresponding result if we close the system into a ring? Is it still bounded by the number of open modes? Or is it unbounded as in the semi-classical (Drude) analysis? It turns out that the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. The non-universal structures and the sparsity of the perturbation matrix cannot be ignored.
In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical threefolds.
We determined the magnetic B-T phase diagram of PdFe bilayer on Ir(111) surface by performing Monte Carlo and spin dynamics simulations based on an effective classical spin model. The parameters of the spin model were determined by ab initio methods. At low temperatures we found three types of ordered phases, while at higher temperatures, below the completely disordered paramagnetic phase, a large region of the phase diagram is associated with a fluctuation-disordered phase. Within the applied model, this state is characterized by the presence of skyrmions with finite lifetime. According to the simulations, this lifetime follows the Arrhenius law as a function of temperature.
We assemble a catalogue of 488 spectroscopically confirmed very high ($z\geq5.00$) redshift quasars and report their near- ($ZYJHK_{s}/K$) and mid- (WISE W1234) infrared properties. 97\% of the VH$z$Q sample is detected in one or more NIR ($ZYJHK/K_{s}$) band, with lack of coverage rather than lack of depth being the reason for the non-detections. 389 (80\%) of the very high redshift quasars are detected at 3.4$\mu$m in the W1 band from the unWISE catalog and all of the $z\geq7$ quasars are detected in both unWISE W1 and W2. Using archival WFCAM/UKIRT and VIRCAM/VISTA data we check for photometric variability that might be expected from super-Eddington accretion. We find 28 of the quasars have sufficient NIR measurements and signal-to-noise ratio to look for variability. Weak variability was detected in multiple bands of SDSS J0959+0227, and very marginally in the $Y$-band of MMT J0215-0529. Only one quasar, SDSS J0349+0034, shows significant differences between WFCAM and VISTA magnitudes in one band. With supermassive black hole accretion likely to be redshift invariant up to very high-redshift, further monitoring of these sources is warranted. All the data, analysis codes and plots used and generated here can be found at: https://github.com/d80b2t/VHzQ}{\tt github.com/d80b2t/VHzQ.
Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of $U$-statistics obeying to Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.
We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{\'e}vy stable jump length distributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method of images leads to a result, which violates a theorem due to Sparre Andersen, according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density (FPTD) governed by the universal long-time decay $\sim t^{-3/2}$. Conversely, we show that for LFs the direct definition known from Gaussian processes in fact defines the probability density of first arrival, which for LFs differs from the FPTD. Our findings are corroborated by numerical results.
Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term \mu for the adjoint matter, eventually decoupling the adjoint matter in the limit of large \mu. If one starts from a large value of the parameter \xi\sim\mu m, where the original theory is at weak coupling, and decreases \xi one hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$.
We derive the upper bounds on certain products of R-parity- and lepton-flavor-violating couplings from $B^\pm \to l^\pm \nu$ decays. These modes of B-meson decays can constrain the product combinations of the couplings with one or more heavy generation indices which are comparable with or stronger than the present bounds. And we investigate the possible effects of R-parity violating interactions on $B_c \to l \nu$ decays. These decay modes can be largely affected by R-parity violation.
The weak antiferromagnetism of URu${}_{2}$Si${}_{2}$ is discussed on the basis of a duality model which takes into account salient features of both itinerant fermions and "localized" component of spin degrees of freedom. The problem is analyzed in the framework of induced-moment mechanism by taking a singlet-singlet crystal field scheme together with the nesting property of partial Fermi surface of itinerant fermions . It is shown that the extremely small ordered moment $m$ of ${\cal O}$($10^{-2}$$\times$$\mu_{B}$) can be compatible with the large specific-heat jump at the transition temperature $T_{N}$. Analysis performed in the presence of external magnetic field shows that the field dependence of $m$ in the limit T\to 0 and T_{N}$ do not scale except very near the critical field B which is consistent with a recent observation by Mentink. It is also shown that the antiferromagnetic magnetic order gives rise to a tiny amount of antiferromagnetic orbital order of f-electrons.
The mixing of three and four massive neutrinos is considered. It is shown that the neutrino oscillation data are not compatible with a hierarchy of couplings in the three-neutrino case. In the case of four neutrinos, a hierarchy of masses is not favored by the data. Only two schemes with two pairs of close masses separated by a gap of the order of 1 eV can accommodate the results of all experiments. If the existing indications in favor of neutrino oscillations will be confirmed, it will mean that the general features of neutrino mixing are quite different from those of quark mixing.
We study solution X of the stochastic equation X = AX +B, where A is a random matrix and B,X are random vectors, the law of (A,B) is given and X is independent of (A,B). The equation is meant in law, the matrix A is 2x2 upper triangular, A_{11}=A_{22}>0, A_{12} is real. A sharp asymptotics of the tail of X =(X _1,X_2) is obtained. We show that under "so called" Kesten-Goldie conditions P (X_2>t)\sim t^{-a} and P (X_1>t )\sim t^{-a}(\log t)^b, where b =a or a\2.
We discuss a new method of integration over matrix variables based on a suitable gauge choice in which the angular variables decouple from the eigenvalues at least for a class of two-matrix models. The calculation of correlation functions involving angular variables is simple in this gauge. Where the method is applicable it also gives an extremely simple proof of the classical integration formula used to reduce multi-matrix models to an integral over the eigenvalues.
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
We use multi-band spatially resolved photometry from the Cosmic Assembly Near-IR Deep Legacy Survey (CANDELS) in the 4 MSec Chandra Deep Field-South (CDF-S) to explore the nuclear and extended colors, color gradients and stellar populations of X-ray selected AGN host galaxies out to z=3. Based on a study of their central light, we develop X-ray based criteria to exclude objects with strong AGN contamination. We use stellar masses from the FIREWORKS database to understand and account for stellar mass selection effects, and carefully study, for the first time, the resolved host galaxy properties of AGNs at z~2 in their rest-frame optical light without substantial nuclear contamination. AGN hosts span a sizable range of stellar masses, colors and color gradients at these redshifts. Their colors, color gradients and stellar population properties are very similar to inactive galaxies of the same stellar mass. At z~1, we find a slightly narrower range in host colors compared to inactive galaxies, as well as hints of more recent star-formation. These differences are weaker or non-existent among AGN hosts at z~2. We discuss the importance of AGN driven feedback in the quenching of galaxies at z>~1 and speculate on possible evolution in the relationship between black hole accretion and the host galaxy towards high redshifts.
Microwave observations of quasi-periodic pulsations (QPP) in multi-timescales are confirmed to be associated with an X3.4 flare/CME event at Solar Broadband Radio Spectrometer in Huairou (SBRS/Huairou) on 13 December 2006. It is most remarkable that the timescales of QPPs are distributed in a broad range from hecto-second (very long period pulsation, VLP, the period P>100 s), deca-second (long period pulsation, LPP, 10<P<100 s), few seconds (short period pulsation, SPP, 1<P<10 s), deci-second (slow-very short period pulsation, slow-VSP, 0.1<P<1.0 s), to centi-second (fast-very short period pulsation, fast-VSP, P<0.1 s), and forms a broad hierarchy of timescales. The statistical distribution in logarithmic period-duration space indicates that QPPs can be classified into two groups: group I includes VLP, LPP, SPP and part of slow-VSPs distributed around a line approximately; group II includes fast-VSP and most of slow-VSP dispersively distributed away from the above line. This feature implies that the generation mechanism of group I is different from group II. Group I is possibly related with some MHD oscillations in magnetized plasma loops in the active region, e.g., VLP may be generated by standing slow sausage mode coupling and resonating with the underlying photospheric 5-min oscillation, the modulation is amplified and forms the main framework of the whole flare/CME process; LPP, SPP, and part of slow-VSPs are most likely to be caused by standing fast modes or LRC-circuit resonance in current-carrying plasma loops. Group II is possibly generated by modulations of resistive tearing-mode oscillations in electric current-carrying flaring loops.
Essentially a biometric system is a pattern recognition system which recognizes a user by determining the authenticity of a specific anatomical or behavioral characteristic possessed by the user. With the ever increasing integration of computers and Internet into daily life style, it has become necessary to protect sensitive and personal data. This paper proposes a multimodal biometric system which incorporates more than one biometric trait to attain higher security and to handle failure to enroll situations for some users. This paper is aimed at investigating a multimodal biometric identity system using Linear Discriminant Analysis as backbone to both facial and speech recognition and implementing such system in real-time using SignalWAVE.