ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the impact parameter dependence of inelasticity in the framework of an updated geometrical model for multiplicity distribution. A formula in which the inelasticity is related to the eikonal is obtained. This framework permits a calculation of the multiplicity distributions as well as the inelasticity once the eikonal function is given. Adopting a QCD inspired parametrization for the eikonal, in which the gluon-gluon contribution dominates at high energy and determines the asymptotic behavior of the cross sections, we find that the inelasticity decreases as collision energy is increased. Our results predict the KNO scaling violation observed at LHC energies by CMS Collaboration.
We define the Schramm-Loewner evolution (SLE) in multiply connected domains for kappa \leq 4 using the Brownian loop measure. We show that in the case of the annulus, this is the same measure obtained recently by Dapeng Zhan. We use the loop formulation to give a different derivation of the partial differential equation for the partition function for the annulus.
Both types of long and short gamma ray bursts involve a stage of a hyper-Eddington accretion of hot and dense plasma torus onto a newly born black hole. The prompt gamma ray emission originates in jets at some distance from this 'central engine' and in most events is rapidly variable, having a form of spikes and subpulses. This indicates at the variable nature of the engine itself, for which a plausible mechanism is an internal instability in the accreting flow. We solve numerically the structure and evolution of the neutrino-cooled torus. We take into account the detailed treatment of the microphysics in the nuclear equation of state that includes the neutrino trapping effect. The models are calculated for both Schwarzschild and Kerr black holes. We find that for sufficiently large accretion rates (> 10 Msun/s for non-rotating black hole, and >1 Msun/s for rotating black hole, depending on its spin), the inner regions of the disk become opaque, while the helium nuclei are being photodissociated. The sudden change of pressure in this region leads to the development of a viscous and thermal instability, and the neutrino pressure acts similarly to the radiation pressure in sub-Eddington disks. In the case of rapidly rotating black holes, the instability is enhanced and appears for much lower accretion rates. We also find the important and possibly further destabilizing role of the energy transfer from the rotating black hole to the torus via the magnetic coupling.
Let $F$ and $G$ be linear recurrences over a number field $\mathbb{K}$, and let $\mathfrak{R}$ be a finitely generated subring of $\mathbb{K}$. Furthermore, let $\mathcal{N}$ be the set of positive integers $n$ such that $G(n) \neq 0$ and $F(n) / G(n) \in \mathfrak{R}$. Under mild hypothesis, Corvaja and Zannier proved that $\mathcal{N}$ has zero asymptotic density. We prove that $\#(\mathcal{N} \cap [1, x]) \ll x \cdot (\log\log x / \log x)^h$ for all $x \geq 3$, where $h$ is a positive integer that can be computed in terms of $F$ and $G$. Assuming the Hardy-Littlewood $k$-tuple conjecture, our result is optimal except for the term $\log \log x$.
The influence of correlated impurities on the critical behaviour of the 3D Ising model is studied using Monte Carlo simulations. Spins are confined into the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behaviour of this magnetic system. Finite size scaling is used to estimate critical couplings and exponents. Long-range correlated disorder does not affect critical behavior. Asymptotic exponents differ from those of the pure 3D Ising model (3DIS), but it is impossible, with our precision, to distinguish them from the randomly diluted Ising model (RDIS).
The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kuchar decomposition). Extensions of every gauge fixing and the associated Kuchar decomposition to a neighbourhood of the constraint manifold are shown to exist.
We report muon spin relaxation measurements on the magnetic structures of RBaCo_2O_5.5 with R=Y, Tb, Dy, and Ho. Three different phases, one ferrimagnetic and two antiferromagnetic, are identified below 300 K. They consist of different ordered spin state arrangements of high-, intermediate-, and low-spin Co^3+ of CoO_6 octahedra. Phase separation into well separated regions with different spin state order is observed in the antiferromagnetic phases. The unusual strongly anisotropic magnetoresistance and its onset at the FM-AFM phase boundary is explained.
The presence of fallback disks around young neutron stars has been invoked over the years to explain a large variety of phenomena. Here we perform a numerical investigation of the formation of such disks during a supernova explosion, considering both neutron star (NS) and black hole (BH) remnants. Using the public code MESA, we compute the angular momentum distribution of the pre-supernova material, for stars with initial masses M in the range 13 - 40 Msun, initial surface rotational velocities vsurf between 25% and 75% of the critical velocity, and for metallicities Z of 1%, 10% and 100% of the solar value. These pre SN models are exploded with energies E varying between 10^{50} - 3x10^{52} ergs, and the amount of fallback material is computed. We find that, if magnetic torques play an important role in angular momentum transport, then fallback disks around NSs, even for low-metallicity main sequence stars, are not an outcome of SN explosions. Formation of such disks around young NSs can only happen under the condition of negligible magnetic torques and a fine-tuned explosion energy. For those stars which leave behind BH remnants, disk formation is ubiquitous if magnetic fields do not play a strong role; however, unlike the NS case, even with strong magnetic coupling in the interior, a disk can form in a large region of the {Z,M,vsurf,E} parameter space. Together with the compact, hyperaccreting fallback disks widely discussed in the literature, we identify regions in the above parameter space which lead to extended, long-lived disks around BHs. We find that the physical conditions in these disks may be conducive to planet formation, hence leading to the possible existence of planets orbiting black holes.
We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of including an ensemble-average attraction in addition to the usual state-dependent drift, where the particle is supposed to be suspended in a large population of identical ones. A Kramers' type law for the particle's exit from the potential's domains of attraction and a large deviations principle for the self-stabilizing diffusion are proved. It turns out that the exit law for the self-stabilizing diffusion coincides with the exit law of a potential diffusion without self-stabilization and a drift component perturbed by average attraction. We show that self-stabilization may substantially delay the exit from domains of attraction, and that the exit location may be completely different.
Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed "crystal structure prediction problem", and recently developed evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary Xtallography) made an important progress in solving it, enabling efficient and reliable prediction of structures with up to ~40 atoms in the unit cell using ab initio methods. Here we review this methodology, as well as recent progress in analyzing energy landscape of solids (which also helps to analyze results of USPEX runs). We show several recent applications - (1) prediction of new high-pressure phases of CaCO3, (2) search for the structure of the polymeric phase of CO2 ("phase V"), (3) high-pressure phases of oxygen, (4) exploration of possible stable compounds in the Xe-C system at high pressures, (5) exotic high-pressure phases of elements boron and sodium.
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.
Electric generation of spin current via spin Hall effect is of great interest as it allows an efficient manipulation of magnetization in spintronic devices. Theoretically, spin current can be also created by a temperature gradient, which is known as spin Nernst effect. Here, we report spin Nernst effect-induced transverse magnetoresistance in ferromagnet (FM)/non-magnetic heavy metal (HM) bilayers. We observe that the magnitude of transverse magnetoresistance (i.e., planar Nernst signal) in FM/HM bilayers is significantly modified by HM and its thickness. This strong dependence of transverse magnetoresistance on HM evidences the spin Nernst effect in HM; the generation of thermally-induced spin current in HM and its subsequent reflection at the FM/HM interface. Our analysis of transverse magnetoresistance shows that the spin Nernst angles of W and Pt have the opposite sign to their spin Hall angles. Moreover, our estimate implies that the magnitude of the spin Nernst angle would be comparable to that of the spin Hall angle, suggesting an efficient generation of spin current by the spin Nernst effect.
We present new $L^\infty$ a priori estimates for weak solutions of a wide class of subcritical elliptic equations in bounded domains. No hypotheses on the sign of the solutions, neither of the non-linearities are required. This method is based in combining elliptic regularity with Gagliardo-Nirenberg or Caffarelli-Kohn-Nirenberg interpolation inequalities.   Let us consider a semilinear boundary value problem $ -\Delta u= f(x,u),$ in $\Omega,$ with Dirichlet boundary conditions, where $\Omega \subset \mathbb{R}^N $, with $N> 2,$ is a bounded smooth domain, and $f$ is a subcritical Carath\'eodory non-linearity. We provide $L^\infty$ a priori estimates for weak solutions, in terms of their $L^{2^*}$-norm, where $2^*=\frac{2N}{N-2}\ $ is the critical Sobolev exponent.   By a subcritical non-linearity we mean, for instance, $|f(x,s)|\le |x|^{-\mu}\, \tilde{f}(s),$ where $\mu\in(0,2),$ and $\tilde{f}(s)/|s|^{2_{\mu}^*-1}\to 0$ as $|s|\to \infty$, here $2^*_{\mu}:=\frac{2(N-\mu)}{N-2}$ is the critical Sobolev-Hardy exponent. Our non-linearities includes non-power non-linearities. In particular we prove that when $f(x,s)=|x|^{-\mu}\,\frac{|s|^{2^*_{\mu}-2}s}{\big[\log(e+|s|)\big]^\beta}\,,$ with $\mu\in[1,2),$ then, for any $\varepsilon>0$ there exists a constant $C_\varepsilon>0$ such that for any solution $u\in H^1_0(\Omega)$, the following holds $$ \Big[\log\big(e+\|u\|_{\infty}\big)\Big]^\beta\le C _\varepsilon \, \Big(1+\|u\|_{2^*}\Big)^{\, (2^*_{\mu}-2)(1+\varepsilon)}\, . $$
We revisit a result of Uchiyama (1980): given that a certain integral test is satisfied, the rate of the probability that Brownian motion remains below the moving boundary $f$ is asymptotically the same as for the constant boundary. The integral test for $f$ is also necessary in some sense. After Uchiyama's result, a number of different proofs appeared simplifying the original arguments, which strongly rely on some known identities for Brownian motion. In particular, Novikov (1996) gives an elementary proof in the case of an increasing boundary. Here, we provide an elementary, half-page proof for the case of a decreasing boundary. Further, we identify that the integral test is related to a repulsion effect of the three-dimensional Bessel process. Our proof gives some hope to be generalized to other processes such as FBM.
Let X be a K3 surface with a polarization H of degree H^2=2rs and with a primitive Mukai vector (r,H,s). The moduli space of sheaves over X with the isotropic Mukai vector (r,H,s) is again a K3 surface Y.   We prove that Y\cong X, if Picard lattice N(X) has an element h_1 with h_1^2=f(r,s), and the pair (H,h_1) satisfies a finite number of congruence conditions modulo N_i(r,s). These conditions are exactly written and are necessary for Y\cong X, if X is general with rk N(X)=2.   Existence of such criterion is surprising and gives some geometric interpretation of elements in N(X) with negative square. We also desribe all divisorial conditions on moduli of (X,H) which imply Y\cong X.   Thus, here we treat in general problems considered in math.AG/0206158, math.AG/0304415, math.AG/0307355 when H.N(X)=Z was assumed. In general, the results are much more complicated and less efficient.
The mechanism for the generation of a dipole moment due to an external field is presented for the Born-Infeld charged particle. The 'polarizability coefficient' is calculated: it is proportional to the third power of the characteristic length in the Born-Infeld theory. Some physical implications are briefly discussed.
The shell correction is proposed in the improved isospin dependent quantum molecular dynamics (ImIQMD) model, which plays an important role in heavy-ion fusion reactions near Coulomb barrier. By using the ImIQMD model, the static and dynamical fusion barriers, dynamical barrier distribution in the fusion reactions are analyzed systematically. The fusion and capture excitation functions for a series of reaction systems are calculated and compared with experimental data. It is found that the fusion cross sections for neutron-rich systems increase obviously, and the strong shell effects of two colliding nuclei result in a decrease of the fusion cross sections at the sub-barrier energies. The lowering of the dynamical fusion barriers favors the enhancement of the sub-barrier fusion cross sections, which is related to the nucleon transfer and the neck formation in the fusion reactions.
Interstellar dust grains exhibit complex dynamics which is essential for understanding many key interstellar processes that involve dust, including grain alignment, grain growth, grain shattering etc. Grain rotational and translational motions are affected not only by gaseous collisions, but also by interactions with ions, photons, magnetic fields etc. Some of those interactions, e.g. interactions of ions with the dipole electric moment of dust grains, require the quantum nature of the process to be accounted for. Similarly, coupling of rotational and vibrational degrees of freedom in a grain happens due to relaxation processes, among which the process related to nuclear spins frequently is the dominant one. This coupling modifies substantially both the dynamics of rotational and translational motions by inducing grain flips. The flipping averages our certain systematic torques and forces that act on grains. As the rate of flipping is larger for smaller grains, these grains can be ``thermally trapped'', i.e. rotate at a thermal rate in spite of the presence of systematic torques. Moreover, a subset of small grains with high dipole moments may rotate at subthermal rates due to high damping arising from grain emission in microwave range of frequencies. Translational dynamics of grains is mostly dominated by grain interactions with magnetohydrodynamic turbulence. Efficient turbulent mixing of dust grains limits the degree to which grains of different sizes may be segregated in space.
We consider dislocations in the framework of Eringen's nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All classical singularities of the Peach-Koehler forces are eliminated. The extremum values of the forces are found near the dislocation line.
Glycolaldehyde is a key molecule in the formation of biologically relevant molecules such as ribose. We report its detection with the Plateau de Bure interferometer towards the Class 0 young stellar object NGC1333 IRAS2A, which is only the second solar-type protostar for which this prebiotic molecule is detected. Local thermodynamic equilibrium analyses of glycolaldehyde, ethylene glycol (the reduced alcohol of glycolaldehyde) and methyl formate (the most abundant isomer of glycolaldehyde) were carried out. The relative abundance of ethylene glycol to glycolaldehyde is found to be ~5 -higher than in the Class 0 source IRAS 16293-2422 (~1), but comparable to the lower limits derived in comets ($\geq$3-6). The different ethylene glycol-to-glycolaldehyde ratios in the two protostars could be related to different CH3OH:CO compositions of the icy grain mantles. In particular, a more efficient hydrogenation on the grains in NGC 1333 IRAS2A would favor the formation of both methanol and ethylene glycol. In conclusion, it is possible that, like NGC 1333 IRAS2A, other low-mass protostars show high ethylene glycol-to-glycolaldehyde abundance ratios. The cometary ratios could consequently be inherited from earlier stages of star formation, if the young Sun experienced conditions similar to NGC1333 IRAS2A.
We show that the magnetoelastic coupling between the magnetization and the amplitude of a short wavelength phonon enables the existence of a first order premartensitic transition from a bcc to a micromodulated phase in $Ni_{2}MnGa$. Such a magnetoelastic coupling has been experimentally evidenced by AC susceptibility and ultrasonic measurements under applied magnetic field. A latent heat around 9 J/mol has been measured using a highly sensitive calorimeter. This value is in very good agreement with the value predicted by a proposed model.
In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively.
Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q-shifted factorials can be incorporated into the implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and Mu to prove nonterminating basic hypergeometric series identities. This observation enables us to extend the q-WZ method to identities on infinite series. As examples, we will give the q-WZ pairs for some classical identities such as the q-Gauss sum, the $_6\phi_5$ sum, Ramanujan's $_1\psi_1$ sum and Bailey's $_6\psi_6$ sum.
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods are constructed differently but are similarly able to detect long-range correlations as well as anomalous diffusion even in the presence of nonstationarities. In this article we describe their similarities in a general framework of detrending methods. We establish this framework independently of the definition of DFA or DMA but by investigating the failure of standard statistical tools applied on nonstationary time series, let these be intrinsic nonstationarities such as for Brownian pathes, or external ones due to additive trends. In particular, we investigate the sample averaged mean squared displacement of the summed time series. By modifying this estimator we introduce a general form of the so-called fluctuation function and can formulate the framework of detrending methods. A detrending method provides an estimator of the fluctuation function which obeys the following principles: The first relates the scaling behaviour of the fluctuation function to the stochastic properties of the time series. The second principles claims unbiasedness of the estimatior. This is the centerpiece of the detrending procedure and ensures that the detrending method can be applied to nonstationary time series, e.g. FBM or additive trends. Both principles are formulated and investigated in detail for DFA and DMA by using the relationship between the fluctuation function and the autocovariance function of the underlying stochastic process of the time series.
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.
We construct a $14$-dimensional affine variety $\Sigma^{14}_{\mathbb{A}}$ with a $\rm{GL}_3$- and a $(\mathbb{C}^*)^6$-actions. We denote by $\Sigma^{13}_{\mathbb{A}}$ the affine variety obtained from $\Sigma^{14}_{\mathbb{A}}$ by setting one specified variable to $1$ (we refer the precise definition to Definition 1.1 of the paper). We show that several weighted projectivizations of $\Sigma^{13}_{\mathbb{A}}$ and $\Sigma^{14}_{\mathbb{A}}$ produce, as weighted complete intersections, examples of prime $\mathbb{Q}$-Fano threefolds of codimension four belonging to $24$ classes of the graded ring database. Except No.360 in the database, these prime $\mathbb{Q}$-Fano threefolds have a Type I Tom projection. Moreover, they are not weighted complete intersections of the cluster variety of type $C_2$ introduced by Coughlan and Ducat. We also show that a partial projectivization of $\Sigma^{14}_{\mathbb{A}}$ has a $\mathbb{P}^2\times \mathbb{P}^2$-fibration over the affine space $\mathbb{A}^9$.