ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The main difficulties are the lack of regularity estimates in the space variable, and the lack of comparison principle due to the non-local term.
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.
Non-Fermi liquid (NFL) behavior in the normal state of the heavy-fermion superconductor UBe13 is studied by means of low-temperature measurements of the specific heat, C, and electrical resistivity, \rho, on a high-quality single crystal in magnetic fields up to 15.5 T. At B=0, unconventional superconductivity forms at Tc=0.9 K out of an incoherent state, characterized by a large and strongly temperature dependent \rho(T). In the magnetic field interval 4 T \leq B \leq 10 T, \rho(T) follows a T^3/2 behavior for Tc(B)\leq T \leq 1 K, while \rho is proportional to T at higher temperatures. Corresponding Non-Fermi liquid behavior is observed in C/T as well and hints at a nearby antiferromagnetic (AF) quantum critical point (QCP) covered by the superconducting state. We speculate that the suppression of short-range AF correlations observed by thermal expansion and specific heat measurements below T_L \simeq 0.7 K (B=0) yields a field-induced QCP, T_L \to 0, at B=4.5 T.
We investigate the possibility of neutrinoless double beta decay ($0\nu\beta\beta$) and leptogenesis within the Alternative Left-Right Model (ALRM). Unlike the usual left-right symmetric model, ALRM features a Majorana right-handed neutrino which does not carry any charge. Further, in this picture the down-type quark and the charged leptons receive mass through the additional left-handed scalar field, rather than the usual doublet. Together, these features conspire to generate significant contributions to the $0\nu\beta\beta$ through vector-scalar ($WH$) mediation. For moderate masses of the relevant charged Higgs boson ($M_{H_1^\pm}\sim 200$ GeV), the half-life of $T_{\frac{1}{2}}^{WH}$ is $\sim 3\times 10^{26}~{\rm yrs}$ for both the case of $^{76}$Ge and $^{136}$Xe, well within the sensitivity expected by future experiments. Invoking the resonant leptogenesis, CP violation arising from the right-handed neutrino decay could be the required order to generate the correct baryogenesis, $\epsilon\sim 10^{-6}$, for small Dirac phases and without any fine tuning.
We present photometry and spectroscopy of PS1-14bj, a hydrogen-poor superluminous supernova (SLSN) at redshift $z=0.5215$ discovered in the last months of the Pan-STARRS1 Medium Deep Survey. PS1-14bj stands out by its extremely slow evolution, with an observed rise of $\gtrsim 125$ rest-frame days, and exponential decline out to $\sim 250$ days past peak at a measured rate of $0.01~{\rm mag~day}^{-1}$, consistent with fully-trapped $^{56}$Co decay. This is the longest rise time measured in a SLSN to date, and the first SLSN to show a rise time consistent with pair-instability supernova (PISN) models. Compared to other slowly-evolving SLSNe, it is spectroscopically similar to the prototype SN2007bi at maximum light, though lower in luminosity ($L_{\rm peak} \simeq 4.6 \times 10^{43} {\rm erg s}^{-1}$) and with a flatter peak than previous events. PS1-14bj shows a number of peculiar properties, including a near-constant color temperature for $>200$ days past peak, and strong emission lines from [O III] $\lambda$5007 and [O III] $\lambda$4363 with a velocity width of $\sim$3400 km/s, in its late-time spectra. These both suggest there is a sustained source of heating over very long timescales, and are incompatible with a simple $^{56}$Ni-powered/PISN interpretation. A modified magnetar model including emission leakage at late times can reproduce the light curve, in which case the blue continuum and [O III] features are interpreted as material heated and ionized by the inner pulsar wind nebula becoming visible at late times. Alternatively, the late-time heating could be due to interaction with a shell of H-poor circumstellar material.
Herschel's PACS instrument observed the environment of the binary system Mira Ceti in the 70 and 160 micron bands. These images reveal bright structures shaped as five broken arcs and fainter filaments in the ejected material of Mira's primary star. The overall shape of the IR emission around Mira deviates significantly from the expected alignment with Mira's exceptionally high space velocity. The observed broken arcs are neither connected to each other nor are they of a circular shape; they stretch over angular ranges of 80 to 100 degrees. By comparing Herschel and GALEX data, we found evidence for the disruption of the IR arcs by the fast outflow visible in both Halpha and the far UV. Radial intensity profiles are derived, which place the arcs at distances of 6-85" (550 - 8000 AU) from the binary. Mira's IR environment appears to be shaped by the complex interaction of Mira's wind with its companion, the bipolar jet, and the ISM.
We consider the half-wave equation $i u_t=Du-|u|^{\frac{2}{3}}u$ in three dimension and in the mass critical. For initial data $u(t_0,x)=u_0(x)\in H^{1/2}_{rad}(\mathbb{R}^3)$ with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate $\|D^{\frac{1}{2}}u(t)\|_2\sim\frac{C(u_0)}{|t|^{\frac{1}{4}}}$ as $t\rightarrow0^-$.
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit non-ideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is non-existent (a necessary condition for preserving superpositions).
We present a combined photometric and spectroscopic analysis of the star formation history and space density of a sample of 485 luminous, M_V - 5 log h < -20.5, field early-type galaxies at redshifts 0.3 < z < 0.6. The observed b_Jori colours as a function of redshift, mean absorption line strengths and [OII] 3727 emission properties are used to constrain the star formation history of the galaxies. The mean star formation history of the early-type galaxy sample is consistent with an old (z_f>1), passively evolving luminosity-weighted stellar population. Twenty-one percent of the sample possess detectable [OII] 3727 emission consistent with a low level (<1 M_solar/yr) of on-going star formation. Parametric and non-parametric estimates of the space density of the sample are derived. The integrated luminosity density at z ~ 0.4, allowing only for passive luminosity evolution, is in excellent agreement with the local, (<z> = 0.1), luminosity density of early-type galaxies. Overall, the sample properties are consistent with a galaxy formation scenario in which the majority of luminous field early-type galaxies formed at redshifts z>1 and have largely evolved passively since the formation epoch.
The nuclear gross theory, originally formulated by Takahashi and Yamada for the $\beta$-decays, is applied for the electronic-neutrino nucleus reactions, employing a more realistic description to the energetics of the Gamow-Teller resonances. The model parameters are gauged from the most recent experimental data, both for $\beta^-$ decay and electron-capture, separately for even-even, even-odd, odd-odd, odd-even nuclei. The numerical estimates for neutrino-nucleus cross sections agree fairly well with previous evaluations done within the framework of microscopic models. The formalism presented here can be extended to the heavy nuclei mass region, where weak processes are quite relevant, which is of astrophysical interest because of its applications in supernova explosive nucleosynthesis.
We present the first detailed X-ray observations of optically-selected clusters at high redshift. Two clusters, Cl 1324+3011 at z = 0.76 and Cl 1604+4304 at z = 0.90, were observed with XMM-Newton. The optical center of each cluster is coincident with an extended X-ray source whose emission is detected out to a radius of 0.5 Mpc. The emission from each cluster appears reasonably circular, with some indication of asymmetries and more complex morphologies. Similarly to other optically-selected clusters at redshifts of z > 0.4, both clusters are modest X-ray emitters with bolometric luminosities of only Lx = 1.4 - 2.0 x 10^(44) erg/s. We measure gas temperatures of T = 2.88 (+0.71/-0.49) keV for Cl 1324+3011 and 2.51 (+1.05/-0.69) keV for Cl 1604+4304. The X-ray properties of both clusters are consistent with the high-redshift Lx-T relation measured from X-ray-selected samples at z > 0.5. However, based on the local relations, their X-ray luminosities and temperatures are low for their measured velocity dispersions (sigma). The clusters are cooler by a factor of 2 - 9 compared to the local sigma-T relation. We briefly discuss the possible explanations for these results.
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized to allow many paths due to the non-local existence of particles in phase space. This principle allows a physical system to evolve non-locally in phase space while still allowing a representation that uses many classical paths. Whereas a point in phase space represents a classical system's state, I represent the state of a non-local system by a mixed trajectory. This formulation naturally leads to the transactional interpretation for resolving the paradoxes of the measurement problem. This principle also suggests a more flexible framework for formulating theories based on invariant actions and provides a single conceptual framework for discussing many areas of science.
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not.
The present article is an important addition to the nonperturbative formulation of QED with x-steps presented by Gavrilov and Gitman in Phys. Rev. D. 93, 045002 (2016). Here we propose a new renormalization and volume regularization procedures which allow one to calculate and distinguish physical parts of different matrix elements of operators of the current and of the energy-momentum tensor, at the same time relating the latter quantities with characteristics of the vacuum instability. For this purpose, a modified inner product and a parameter {\tau} of the regularization are introduced. The latter parameter can be fixed using physical considerations. In the Klein zone this parameter can be interpreted as the time of the observation of the pair production effect. In the refined formulation of QED with x-steps, we succeeded to consider the backreaction problem. In the case of an uniform electric field E confined between two capacitor plates separated by a finite distance L, we see that the smallness of the backreaction implies a restriction (the consistency condition) on the product EL from above.
Let $X$ be a projective variety over a number field $K$ (resp. over $\mathbb{C}$). Let $H$ be the sum of ``sufficiently many positive divisors'' on $X$. We show that any set of quasi-integral points (resp. any integral curve) in $X-H$ is not Zariski dense.
We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a uniform density $\rho_-=1$, Johansson showed the equivalence of the current fluctuation of ASEP and the largest eigenvalue distribution of random matrices. We extend Johansson's formula and derive modified ensembles of random matrices, corresponding to general ASEP initial conditions. Taking the scaling limit, we find that a phase change of the asymptotic current fluctuation occurs at a critical position.
The development of valleytronics demands long-range electronic transport with preserved valley index, a degree of freedom similar to electron spin. A promising structure for this end is a topological one-dimensional (1D) channel formed in bilayer graphene (BLG) under special electrostatic conditions or specific stacking configuration, called domain wall (DW). In these 1D channels, the valley-index defines the propagation direction of the charge carriers and the chiral edge states (kink states) are robust over many kinds of disorder. However, the fabrication of DWs is challenging, requiring the design of complex multi-gate structures or have been producing on rough substrates, showing a limited mean free path. Here, we report on a high-quality DW formed at the curved boundary of folded bilayer graphene (folded-BLG). At such 1D conducting channel we measured a two-terminal resistance close to the quantum resistance $R = e^2/4h$ at zero magnetic field, a signature of kink states. Our experiments reveal a long-range ballistic transport regime that occurs only at the DW of the folded-BLG, while the other regions behave like semiconductors with tunable band gap.
The next-to-leading order (NLO) QCD radiative corrections to W+W- production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total W+W- cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross section is the most precise theoretical prediction available. Uncertainties due to scale variation are shown to be small when the threshold logarithms are included. NNLL threshold resummation increases the W+W- invariant mass distribution by ~ 3-4% in the peak region for both \sqrt{S}=8 and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections increase the NLO cross section by 0.5-3% for \sqrt{S}=7, 8, 13, and 14 TeV.
A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D-dimensions. It is found that these models, to {\it all} orders in the inverse fermi mass, bosonise to a theory involving a usual gauge field and a (D-2) rank antisymmetric (Kalb-Ramond) tensor field. Explicit bosonisation identities for the fermion current are deduced. Specialising to the lowest order reveals (for any $D \geq 4$) a mapping between the massive Thirring model and the Proca model. It also establishes an exact duality between the Proca model and the massive (D-2) rank Kalb-Ramond model. Schwinger terms in the current algebra are computed. Conventional bosonisation results in D=2, 3 are reproduced.
We have evaluated the contribution of the AGN population to the ionization history of the Universe based on a semi-analytic model of galaxy formation and evolution in the CDM cosmological scenario. The model connects the growth of black holes and of the ensuing AGN activity to galaxy interactions. In the model we have included a self consistent physical description of the escape of ionizing UV photons; this is based on the blast-wave model for the AGN feedback we developed in a previous paper to explain the distribution of hydrogen column densities in AGNs of various redshifts and luminosities, due to absorption by the host galaxy gas. The model predicts UV luminosity functions for AGNs which are in good agreement with those derived from the observations especially at low and intermediate redshifts (z=3). At higher redshifts (z>5) the model tends to overestimate the data at faint luminosities. Critical biases both in the data and in the model are discussed to explain such apparent discrepancies. The predicted hydrogen photoionization rate as a function of redshift is found to be consistent with that derived from the observations. All that suggests to reconsider the role of the AGNs as the main driver of the ionization history of the Universe.
Using the multi-instrument observations, we make the first simultaneous imaging and spectral study on the null point of a fan-spine magnetic topology during a solar flare. When magnetic reconnection occurs at the null point, the fan-spine configuration brightens in the (extreme-)ultraviolet channels. In the H$\alpha$ images, the fan-spine structure is partly filled and outlined by the bi-directional material flows ejected from the reconnection site. The extrapolated coronal magnetic field confirms the existence of the fan-spine topology. Before and after the flare peak, the total velocity of the outflows is estimated to be about 60 km s$^{-1}$. During the flare, the Si IV line profile at the reconnection region is enhanced both in the blue-wing and red-wing. At the flare peak time, the total velocity of the outflows is found to be 144 km s$^{-1}$. Superposed on the Si IV profile, there are several deep absorption lines with the blueshift of several tens of km s$^{-1}$. The reason is inferred to be that the bright reconnection region observed in Si IV channel is located under the cooler material appearing as dark features in the H$\alpha$ line. The blueshifted absorption lines indicate the movement of the cooler material toward the observer. The depth of the absorption lines also depends on the amount of cooler material. These results imply that this kind of spectral profiles can be used as a tool to diagnose the properties of cooler material above reconnection site.
We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A_y, for p-3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E_{c.m.} = 1.20 MeV and by 40% at E_{c.m.} = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) Hyperspherical Harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. In a previous paper, we established that these systems admit traveling wave solutions. It is then natural to investigate their asymptotic distributions. This is the main object of this paper. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.
In a recent work, the present author generalized a fundamental result of Gauss related to quadratic reciprocity, and also showed that the above result of Gauss is equivalent to a special case of a well-known result of Sylvester related to the Frobenius coin problem. In this note, we use this equivalence to show that the above generalization of the result of Gauss naturally leads to an interesting generalization of the result of Sylvester. To be precise, for given positive coprime integers $a$ and $b$, and for a family of values of $k$ in the interval $0 \leq k < (a-1)(b-1)$, we find the number of nonnegative integers $\leq k$ that can be expressed in the form $ax+by$ for nonnegative integers $x$ and $y$. We also give an elementary proof of Eisenstein's Lemma for Jacobi symbols using floor function sums. Our proof provides a natural straightforward generalization of the Gauss-Eisenstein proof of the law of quadratic reciprocity for Jacobi symbols.
The purpose of this article is to solve rough differential equations with the theory of regularity structures. These new tools recently developed by Martin Hairer for solving semi-linear partial differential stochastic equations were inspired by the rough path theory. We take a pedagogical approach to facilitate the understanding of this new theory. We recover results of the rough path theory with the regularity structure framework. Hence, we show how to formulate a fixed point problem in the abstract space of modelled distributions to solve the rough differential equations. We also give a proof of the existence of a rough path lift with the theory of regularity structure.