ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the incompressible Navier-Stokes equation with a fractional power $\alpha\in[1,\infty)$ of the Laplacian in the three dimensional case. We prove the existence of a smooth solution with arbitrarily small in $\dot{B}_{\infty,p}^{-\alpha}$ ($2<p \leq \infty$) initial data that becomes arbitrarily large in $\dot{B}_{\infty,\infty}^{-s}$ for all $s> 0$ in arbitrarily small time. This extends the result of Bourgain and Pavlovi\'{c} for the classical Navier-Stokes equation which utilizes the fact that the energy transfer to low modes increases norms with negative smoothness indexes. It is remarkable that the space $\dot{B}_{\infty,\infty}^{-\alpha}$ is supercritical for $\alpha >1$. Moreover, the norm inflation occurs even in the case $\alpha \geq 5/4$ where the global regularity is known.
We denote by $\text{ex}(n, H, F)$ the maximum number of copies of $H$ in an $n$-vertex graph that does not contain $F$ as a subgraph. Recently, Grzesik, Gy\H{o}ri, Salia, Tompkins considered conditions on $H$ under which $\text{ex}(n, H, K_r)$ is asymptotically attained at a blow-up of $K_{r-1}$, and proposed a conjecture. In this note we disprove their conjecture.
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. The latter has the same generator as the Markov process along the branches plus additional jumps, associated with branching events of accelerated rate and biased distribution. This comes from the fact that choosing an individual uniformly at time t favors lineages with more branching events and larger offspring number. The central limit theorem is considered on a special case. Several examples are developed, including applications to splitting diffusions, cellular aging, branching L\'{e}vy processes.
Galactic disks consist of both stars and gas. The gas is more dynamically responsive than the stars, and strongly nonlinear structures and velocities can develop in the ISM even while stellar surface density perturbations remain fractionally small. We use 2D numerical simulations to explore formation of bound clouds and turbulence generation in the gas of two-component galactic disks. We represent the stars with collisionless particles and follow their orbits using a PM method, and treat the gas as an isothermal, unmagnetized fluid. The two components interact through a combined gravity. Using stellar parameters typical of mid-disk conditions, we find that models with gaseous Toomre parameter Q_g < Q_c ~ 1.4 experience gravitational runaway and eventually form bound condensations. This Q_c value is nearly the same as previously found for razor-thin, gas-only models, indicating that the destabilizing effect of live stars is offsets the reduced self-gravity of thick disks. This result is also consistent with empirical studies showing that star formation is suppressed when Q_g > 1-2. The bound gaseous clouds that form have mass 6x10^7 Msun each; these represent superclouds that would subsequently fragment into GMCs. Self-gravity and sheared rotation also interact to drive turbulence in the gas when Q_g > Q_c. This turbulence is anisotropic, with more power in sheared than compressive motions. The gaseous velocity dispersion is ~ 0.6 times the thermal speed when Q_g ~ Q_c. This suggests that gravity is important in driving ISM turbulence in many spiral galaxies, since the low efficiency of star formation naturally leads to a state of marginal instability.
In the supersymmetric framework, a higgsino asymmetry exists in the universe before the electroweak phase transition. We investigate whether the higgsino is a viable asymmetric dark matter candidate. We find that this is indeed possible. The gauginos, squarks and sleptons must all be very heavy, such that the only electroweak-scale superpartners are the higgsinos. The temperature of the electroweak phase transition must be in the (1-10) GeV range.
Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.
The detectors of the international gravitational-wave (GW) observatory network are currently taking data with sensitivities improved via squeezing the photon counting noise of the laser light used. Several GW candidate events, such as black-hole mergers, are already in the pipeline to be analyzed in detail. While the brand-new field of GW astronomy relies on squeezed light for reaching higher sensitivities, the physical understanding of such light, although being well-described by quantum theory, is still under discussion. Here, I present a description of why squeezed light, as now being exploited by GW observatories, constitutes rather remarkable physics. I consider the squeezed photon statistics and show its relation to the famous gedanken experiment formulated by Einstein, Podolsky, and Rosen in 1935. My description illuminates 'quantum weirdness' in a clear way and might be the starting point for finding the physics of quantum correlations in general, which scientists have been seeking for decades.
We study the alignment of dark matter haloes with the cosmic web characterized by the tidal and velocity shear fields. We focus on the alignment of their shape, angular momentum and peculiar velocities. We use a cosmological N-body simulation that allows to study dark matter halos spanning almost five orders of magnitude in mass ($10^{9}$-$10^{14}$) $h^{-1}$$M_{\odot}$ and spatial scales of $(0.5$-$1.0)$ $h^{-1}$ Mpc to define the cosmic web. We find that the halo shape presents the strongest alignment along the smallest tidal eigenvector, e.g. along filaments and walls, with a signal that gets stronger as the halo mass increases. In the case of the velocity shear field only massive halos $>10^{12}$ $h^{-1}$$M_{\odot}$ tend to have their shapes aligned along the largest tidal eigenvector; that is, perpendicular to filaments and walls. For the angular momentum we find alignment signals only for halos more massive than $10^{12}$ $h^{-1}$$M_{\odot}$ both in the tidal and velocity shear webs where the preferences are for it to be parallel to the middle eigenvector; perpendicular to filaments and parallel to walls. Finally, the peculiar velocities show a strong alignment along the smallest tidal eigenvector for all halo masses; halos move along filaments and walls. In the velocity shear the same alignment is present but weaker and only for haloes less massive than $10^{12}$ $h^{-1}$$M_{\odot}$. Our results clearly show that the two different algorithms we used to define the cosmic web describe different physical aspects of non-linear collapse and should be used in a complementary way to understand the effect of the cosmic web on galaxy evolution.
A twistorial formulation of the N=1 D=4 superparticle with tensorial central charges describing massive and massless cases in uniform manner is given. The twistors resolve energy-momentum vector whereas the tensorial central charges are written in term of spinor Lorentz harmonics. The model makes possible to describe states preserving all allowed fractions of target-space supersymmetry. The full analysis of the number of conserved supersymmetries in models with N=1 D=4 superalgebra with tensorial central charges has been carried out.
Optical transitions of an Er$_2$O$_3$ film on a Si substrate grown by using a metal-organic chemical vapor deposition technique were investigated in a wide temperature (300 K $\sim$ 5 K) and spectral (500 nm and 850 nm) ranges. Numerous sharp transitions corresponding to the Er$^{3+}$ ionic levels were observed, which show Stark shifts induced by the crystal field. With decreasing temperature from 300 K to 5 K, all transition peaks exhibit spectral red-shift. We believe that such red-shift behavior is due to the change of the crystal field together with the change of strain field induced by the film and the substrate in varying temperature. An interesting result is the total amount of red-shifts between 300 K and 5 K. We obtain that the higher transition energy peaks show bigger red-shifts. This is very consistent to all transition peaks. This is because the dipole moments between the transition levels are different that lead to different amounts of Stark shifts.
We demonstrate that the half-doped bilayer manganite La_{1}Sr_{2}Mn_{2}O_{7} exhibits CE-type charge-ordered and spin-ordered states below $T_{N, CO}^A = 210$ K and below $T_{N}^{CE} \sim 145$ K, respectively. However, the volume fraction of the CE-type ordering is relatively small, and the system is dominated by the A-type spin ordering. The coexistence of the two types of ordering is essential to understand its transport properties, and we argue that it can be viewed as an effective phase separation between the metallic $d(x^{2}-y^{2})$ orbital ordering and the charge-localized $d(3x^{2}-r^{2})/d(3y^{2}-r^{2})$ orbital ordering.
The disk corona evaporation model extensively developed for the interpretation of observational features of black hole X-ray binaries (BHXRBs) is applied to AGNs. Since the evaporation of gas in the disk can lead to its truncation for accretion rates less than a maximal evaporation rate, the model can naturally account for the soft spectrum in high luminosity AGNs and the hard spectrum in low luminosity AGNs. The existence of two different luminosity levels describing transitions from the soft to hard state and from the hard to soft state in BHXRBs, when applied to AGNs, suggests that AGNs can be in either spectral state within a range of luminosities. For example, at a viscosity parameter, \alpha, equal to 0.3, the Eddington ratio from the hard to soft transition and from the soft to hard transition occurs at 0.027 and 0.005 respectively. When the Eddington ratio of the AGN lies below the critical value corresponding to its evolutionary state, the disk is truncated. With decreasing Eddington ratios, the inner edge of the disk increases to greater distances from the black hole with a concomitant increase in the inner radius of the broad line region, $R_{BLR}$. The absence of an optically thick inner disk at low luminosities gives rise to region in the size of borad line-luminosity plane for which the relation $R_{BLR} \propto L^{1/2}$ inferred at high luminosities is excluded. As a result, a lower limit to the accretion rate is predicted for the observability of broad emission lines, if the broad line region is associated with an optically thick accretion disk. Thus, true Seyfert 2 galaxies may exist at very low accretion rates/luminosities. The differences between BHXRBs and AGNs in the framework of the disk corona model are discussed and possible modifications to the model are briefly suggested.
In this article, we define a family of regular bipartite graphs and show that the homotopy type of the independence complexes of this family is the wedge sum of spheres of certain dimensions.
In the context of SUSY grand unification a link is established between the hadronic and leptonic soft breaking sectors. Such relation is here exploited in particular for FCNC processes in B physics. It is shown how bounds on leptonic FCNC involving the third generation translate into constraints on FC B decays. In the second part of the contribution we show that tests of lepton universality in K and B decays can represent an interesting handle to obtain relevant information on the amount of FCNC in the second and third fermion generation.
We use Khovanov and Kuperberg's web growth rules to identify the minimal term in the invariant associated to an $\text{SL}_3$ web diagram, with respect to a particular term order.
We examine millisecond magnetars as central engines of Gamma Ray Bursts' (GRB) prompt emission. Using the proto-magnetar wind model of Metzger et al. 2011, we estimate the temporal evolution of the magnetization and power injection at the base of the GRB jet and apply these to different prompt emission models to make predictions for the GRB energetics, spectra and lightcurves. We investigate both shock and magnetic reconnection models for the particle acceleration, as well as the effects of energy dissipation across optically thick and thin regions of the jet. The magnetization at the base of the jet, $\sigma_0$, is the main parameter driving the GRB evolution in the magnetar model and the emission is typically released for $100\lesssim \sigma_0 \lesssim 3000$. Given the rapid increase in $\sigma_0$ as the proto-magnetar cools and its neutrino-driven mass loss subsides, the GRB duration is typically limited to $\lesssim 100$ s. This low baryon loading at late times challenges magnetar models for ultra-long GRBs, though black hole models likely run into similar difficulties without substantial entrainment from the jet walls. The maximum radiated gamma-ray energy is $\lesssim 5 \times 10^{51}$erg, significantly less than the magnetar's total initial rotational energy and in strong tension with the high end of the observed GRB energy distribution. However, the gradual magnetic dissipation model (Beniamini & Giannios 2017) applied to a magnetar central engine, naturally explains several key observables of typical GRBs, including energetics, durations, stable peak energies, spectral slopes and a hard to soft evolution during the burst.
There is now strong evidence that many low-luminosity AGNs (LLAGNs) contain accreting massive black holes and that the nuclear radio emission is dominated by parsec-scale jets launched by these black holes. Here, we present preliminary results on the 1.4 GHz to 667 GHz spectral shape of a well-defined sample of 16 LLAGNs. The LLAGNs have a falling spectrum at high GHz frequencies. Several also show a low-frequency turnover with a peak in the 1-20 GHz range. The results provide further support for jet dominance of the core radio emission. The LLAGNs show intriguing similarities with gigahertz-peaked spectrum (GPS) sources.
A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory is the mean time of the embryo formation. On the base of this time the probability to observe the embryo formed during the given time is estimated which allows to construct a simple approximate theory.
For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well know that the stochastic exponential of this stochastic integral is a local martingale. In this paper we consider the case of an arbitrary Borel measurable function b where it may not be possible to define the stochastic integral of b(Y) directly. However the notion of the stochastic exponential can be generalized. We define a non-negative process Z, called generalized stochastic exponential, which is not necessarily a local martingale. Our main result gives deterministic necessary and sufficient conditions for Z to be a local, true or uniformly integrable martingale.
Sheet-like clouds are common in turbulent gas and perhaps form via collisions between turbulent gas flows. Having examined the evolution of an isothermal shocked slab in an earlier contribution, in this work we follow the evolution of a sheet-like cloud confined by (thermal)pressure and gas in it is allowed to cool. The extant purpose of this endeavour is to study the early phases of core-formation. The observed evolution of this cloud supports the conjecture that molecular clouds themselves are three-phase media (comprising viz. a stable cold and warm medium, and a third thermally unstable medium), though it appears, clouds may evolve in this manner irrespective of whether they are gravitationally bound. We report, this sheet fragments initially due to the growth of the thermal instability and some fragments are elongated, filament-like. Subsequently, relatively large fragments become gravitationally unstable and sub-fragment into smaller cores. The formation of cores appears to be a three stage process : first, growth of the thermal instability leads to rapid fragmentation of the slab; second, relatively small fragments acquire mass via gas-accretion and/or merger and third, sufficiently massive fragments become susceptible to the gravitational instability and sub-fragment to form smaller cores. We investigate typical properties of clumps (and smaller cores) resulting from this fragmentation process. Findings of this work support the suggestion that the weak velocity field usually observed in dense clumps and smaller cores is likely seeded by the growth of dynamic instabilities. Simulations were performed using the smooth particle hydrodynamics algorithm.
The measured spin-down rates in quiescence of the transient accreting millisecond pulsars IGR J00291+5934, XTE J1751-305, SAX J1808.4-3658, and Swift J1756.9-2508 have been used to estimate the magnetic moments of these objects assuming standard magnetic dipole braking. It is shown that this approach leads to an overestimate, if the amount of residual accretion is enough to distort the magnetosphere away from a force-free configuration, through magnetospheric mass loading or crushing, so that the lever arm of the braking torque migrates inside the light cylinder. We derive an alternative spin-down formula and calculate the residual accretion rates where the formula is applicable. As a demonstration, we apply the alternative spin-down formula to produce updated magnetic moment estimates for the four objects above. We note that, based on current uncertain observations of quiescent accretion rates, magnetospheric mass loading and crushing are neither firmly indicated nor ruled out in these four objects. Because quiescent accretion rates are not measured directly (only upper limits are placed), it is impossible to be confident without more data whether the thresholds for magnetospheric mass loading or crushing are reached or not.
We point out that the measurement of just the two branching fractions \linebreak $B(K^+\to\pi^+\nu\bar\nu)$ and $B(K_L\to\pi^0\nu\bar\nu)$ can in a theoretically clean manner determine $\sin 2\beta$ almost independently of $m_t$ and $V_{cb}$. This allows to obtain an interesting relation between the CP asymmetry $A_{CP}(\psi K_S)$ in B physics and the branching ratios for these two rare K decays. The recently calculated next-to-leading order QCD corrections improve the accuracy of this analysis. We find typically $\Delta\sin 2\beta=\pm 0.11$ provided $B(\kpn)$ and $B(\klpn)$ are measured within $\pm 10\%$ accuracy. With decreasing uncertainty in $\Lambda_{\overline{MS}}$ and $m_c$ this error could be reduced to $\Delta\sin 2\beta < \pm 0.10$. The determination of $\sin 2\alpha$ and $\sin 2\gamma$ on the other hand is rather poor. However respectable determinations of the Wolfenstein parameter $\eta$ and of $\mid V_{td}\mid$ can be obtained.
The existence of a rotational band with the $\alpha$+$^{12}$C($0_2^+$) cluster structure, in which three $\alpha$ particles in $^{12}$C($0_2^+$) are locally condensed, is demonstrated near the four-$\alpha$ threshold of $^{16}$O in agreement with experiment. This is achieved by studying structure and scattering for the $\alpha$+$^{12}$C($0_2^+$) system in a unified way. A drastic reduction (quenching) of the moment of the inertia of the $0^+$ state at 15.1 MeV just above the four-$\alpha$ threshold in $^{16}$O suggests that it could be a candidate for the superfluid state in $\alpha$-particle condensation.
Large-scale structure formation, accretion and merging processes, AGN activity produce cosmological gas shocks. The shocks convert a fraction of the energy of gravitationally accelerated flows to internal energy of the gas. Being the main gas-heating agent, cosmological shocks could amplify magnetic fields and accelerate energetic particles via the multi-fluid plasma relaxation processes. We first discuss the basic properties of standard single-fluid shocks. Cosmological plasma shocks are expected to be collisionless. We then review the plasma processes responsible for the microscopic structure of collisionless shocks. A tiny fraction of the particles crossing the shock is injected into the non-thermal energetic component that could get a substantial part of the ram pressure power dissipated at the shock. The energetic particles penetrate deep into the shock upstream producing an extended shock precursor. Scaling relations for postshock ion temperature and entropy as functions of shock velocity in strong collisionless multi-fluid shocks are discussed. We show that the multi-fluid nature of collisionless shocks results in excessive gas compression, energetic particle acceleration, precursor gas heating, magnetic field amplification and non-thermal emission. Multi-fluid shocks provide a reduced gas entropy production and could also modify the observable thermodynamic scaling relations for clusters of galaxies.
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with a non-trivial topology are studied. This paper discusses the special class of the so-called double-action manifolds, which are for the first time analysed with respect to their CMB anisotropies. The CMB anisotropies are computed for all prism double-action manifolds generated by a binary dihedral and a cyclic group with a group order of up to 180 leading to 33 different topologies. Several spaces are found which show a suppression of the CMB anisotropies on large angular distances as it is found on the real CMB sky. It turns out that two of these spaces possess Dirichlet domains which are not very far from highly symmetric polyhedra like Platonic or Archimedean ones.
Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the operator into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version collects mutually commuting Pauli operators together before measuring all operators within a collection simultaneously. The effectiveness of doing this depends on two factors. Firstly, we must understand the improvement offered by a given arrangement of Paulis in collections. In our work, we propose two natural metrics for quantifying this, operating under the assumption that measurements are distributed optimally among collections so as to minimise the overall finite sampling error. Motivated by the mathematical form of these metrics, we introduce SORTED INSERTION, a collecting strategy that exploits the weighting of each Pauli operator in the overall sum. Secondly, to measure all Pauli operators within a collection simultaneously, a circuit is required to rotate them to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any collection of $k$ independent commuting $n$-qubit Pauli operators using at most $kn-k(k+1)/2$ and $O(kn/\log k)$ two-qubit gates respectively. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the operators in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of collections.