ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included the case where the sample space is time dependent in a previous work \textit{Phys. Rev. E} \textbf{90}, 022125 (2014). We found a general solution through a dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to the one in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work we show how Markov process in general could be linked via gauge (local) transformations and we present some illustrative examples for this results.
Given two graphs $G_1, G_2$, the connected size Ramsey number ${\hat{r}}_c(G_1,G_2)$ is defined to be the minimum number of edges of a connected graph $G$, such that for any red-blue edge colouring of $G$, there is either a red copy of $G_1$ or a blue copy of $G_2$. Concentrating on ${\hat{r}}_c(nK_2,G_2)$ where $nK_2$ is a matching, we generalise and improve two previous results as follows. Vito, Nabila, Safitri, and Silaban obtained the exact values of ${\hat{r}}_c(nK_2,P_3)$ for $n=2,3,4$. We determine its exact values for all positive integers $n$. Rahadjeng, Baskoro, and Assiyatun proved that ${\hat{r}}_c(nK_2,C_4)\le 5n-1$ for $n\ge 4$. We improve the upper bound from $5n-1$ to $\lfloor (9n-1)/2 \rfloor$. In addition, we show a result which has the same flavour and has exact values: ${\hat{r}}_c(nK_2,C_3)=4n-1$ for all positive integers $n$.
A new numerical technique to identify the cosmic web is proposed. It is based on locating multi-stream flows, i.e. the places where the velocity field is multi-valued. The method is local in Eulerian space, simple and computaionally efficient. This technique uses the velocities of particles and thus takes into account the dynamical information. This is in contrast with the majority of standard methods that use the coordinates of particles only. Two quantities are computed in every mesh cell: the mean and variance of the velocity field. In the cells where the velocity is single-valued the variance must be equal to zero exactly, therefore the cells with non-zero variance are identified as multi-stream flows. The technique has been tested in a N-body simulation of the \L CDM model. The preliminary analysis has shown that numerical noise does not pose a significant problem. The web identified by the new method has been compared with the web identified by the standard technique using only the particle coordinates. The comparison has shown overall similarity of two webs as expected, however they by no means are identical. For example, the isocontours of the corresponding fields have significantly different shapes and some density peaks of similar heights exhibit significant differences in the velocity variance and vice versa. This suggest that the density and velocity variance have a significant degree of independence. The shape of the two-dimensional pdf of density and velocity variance confirms this proposition. Thus, we conclude that the dynamical information probed by this technique introduces an additional dimension into analysis of the web.
Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type $p=w_{\rm eff}(\rho)\,\rho$, and has been used in previous works to describe, e.g., a possible scenario for the growth of the dark-energy content of the present Universe. At the classical level the fluid dynamics in a spatially flat Friedmann-Robertson-Walker background implies the existence of two possible equilibrium solutions depending on the model parameters, associated with (asymptotic) finite pressure and energy density. We show that no future cosmological singularity is developed during the evolution for this specific model. The corresponding quantum effects in the late-time behavior of the system are also investigated within the framework of quantum geometrodynamics, i.e., by solving the (minisuperspace) Wheeler-DeWitt equation in the Born-Oppenheimer approximation, constructing wave-packets and analyzing their behavior.
We propose a scheme for implementing quantum algorithms with resonant interactions. Our scheme only requires resonant interactions between two atoms and a cavity mode, which is simple and feasible. Moreover, the implementation would be an important step towards the fabrication of quantum computers in cavity QED system.
We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We give partial characterization of transience and recurrence in the different dimensions. Finally we prove Central Limit Theorem (CLT) for such random walks, under a condition on the distance between coordinate nearest points.
We present two matched sets of five simulations each, covering five presently favored simple modifications to the standard cold dark matter (CDM) scenario. One simulation suite, with a linear box size of 75 Mpc/h, is designed for high resolution and good statistics on the group/poor cluster scale, and the other, with a box size of 300 Mpc/h, is designed for good rich cluster statistics. All runs had 57 million cold particles, and models with massive neutrinos had an additional 113 million hot particles. We consider separately models with massive neutrinos, tilt, curvature, and a nonzero cosmological constant in addition to the standard CDM model. We find that our tilted Omega+Omega_Lambda=1 (TLCDM) model produces too much small-scale power by a factor of ~3, and our open Lambda=0 (OCDM) model also exceeds observed small-scale power by a factor of 2. In addition, we take advantage of the large dynamic range in detectable halo masses our simulations allow to check the shape of the Press-Schechter approximation. We find good fits at cluster masses for delta_c=1.27--1.35 for a Gaussian filter and delta_c=1.57--1.73 for a tophat filter. However, Press-Schechter overpredicts the number density of halos compared to the simulations in the high resolution suite by a weakly cosmology-dependent factor of 1.5--2 at galaxy and group masses, which cannot be fixed by adjusting delta_c within reasonable bounds. An appendix generalizes the spherical collapse model to any isotropic cosmology.
Recent developments of the covariant Bethe-Salpeter (BS) approach with the use of the separable interaction for the deuteron are reviewed. It is shown that the BS formalism allows a covariant description of various electromagnetic reactions like the lepton-deuteron scattering, deuteron electro-disintegration, deep inelastic scattering (DIS) of leptons on light nuclei. The procedure of the construction of the separable nucleon-nucleon (NN) interaction is discussed. The BS formalism facilitates analysis of the role of the P-waves (negative energy components) in the electromagnetic properties of the deuteron and its comparison with the nonrelativistic results. Furthermore the covariant BS approach makes it possible to analyze DIS of leptons from the deuteron in a model independent way and to extend the formalism to DIS reactions on the light nuclei.
Context. Flare Hard X-Rays (HXRs) from non-thermal electrons are commonly treated as solely bremsstrahlung (f-f), recombination (f-b) being neglected. This assumption is shown to be substantially in error, especially in hot sources, mainly due to recombination onto Fe ions.   Aims. We analyse the effects on HXR spectra and electron diagnostics by including non-thermal recombination onto heavy elements in our model.   Methods. Using Kramers hydrogenic cross sections with effective Z, we calculate f-f and f-b spectra for power-law electron spectra, in both thin and thick target limits, and for Maxwellians, with summation over all important ions.   Results. We find that non-thermal electron recombination, especially onto Fe, must, in general, be included together with f-f, for reliable spectral interpretation, when the HXR source is hot. f-b contribution is greatest when the electron spectral index is large, and any low energy cut-off small. f-b spectra recombination edges mean a cut-off in F(E) appears as a HXR feature at Photon energy = Ec + Vz, offering an Ec diagnostic. Including f-b lowers, greatly in some cases, the F(E) needed for prescribed HXR fluxes and, even when small, seriously distorts F(E) as inferred by inversion or forward fitting based on f-f alone.   Conclusions. f-b recombination from non-thermal electrons can be an important contributor to HXR spectra and should be included in spectral analyses, especially for hot sources. Accurate results will require use of better cross sections than ours and consideration of source ionisation structure.
In classical numerical relativity, marginally outer trapped surfaces (MOTSs) are the main tool to locate and characterize black holes. For five decades it has been known that during a binary merger, a new outer horizon forms around the initial apparent horizons of the individual holes once they are sufficiently close together. However the ultimate fate of those initial horizons has remained a subject of speculation. Recent axisymmetric studies have shed new light on this process and this pair of papers essentially completes that line of research: we resolve the key features of the post-swallowing axisymmetric evolution of the initial horizons. This first paper introduces a new shooting-method for finding axisymmetric MOTSs along with a reinterpretation of the stability operator as the analogue of the Jacobi equation for families of MOTSs. Here, these tools are used to study exact solutions and initial data. In the sequel paper they are applied to black hole mergers.
We first present a new stochastic version of the Cucker-Smale model of the emergent behavior in flocks in which the mutual communication between individuals is affected by random factor. Then, the existence and uniqueness of global solution to this system are verified. We show a result which agrees with natural fact that under the effect of large noise, there is no flocking. In contrast, if noise is small, then flocking may occur. Paper ends with some numerical examples.
We give a short new proof of a version of the Kruskal-Katona theorem due to Lov\'asz. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a question of Mubayi. This in turn leads to another combinatorial proof of a stability theorem for intersecting families, which was originally obtained by Friedgut using spectral techniques and then sharpened by Keevash and Mubayi by means of a purely combinatorial result of Frankl. We also give an algebraic perspective on these problems, giving yet another proof of intersection stability that relies on expansion of a certain Cayley graph of the symmetric group, and an algebraic generalisation of Lov\'asz's theorem that answers a question of Frankl and Tokushige.
The Kelvin-Helmholtz instability is well known to be capable of converting well-ordered flows into more disordered, even turbulent, flows. As such it could represent a path by which the energy in, for example, bowshocks from stellar jets could be converted into turbulent energy thereby driving molecular cloud turbulence. We present the results of a suite of fully multifluid magnetohydrodynamic simulations of this instability using the HYDRA code. We investigate the behaviour of the instability in a Hall dominated and an ambipolar diffusion dominated plasma as might be expected in certain regions of accretion disks and molecular clouds respectively.   We find that, while the linear growth rates of the instability are unaffected by multifluid effects, the non-linear behaviour is remarkably different with ambipolar diffusion removing large quantities of magnetic energy while the Hall effect, if strong enough, introduces a dynamo effect which leads to continuing strong growth of the magnetic field well into the non-linear regime and a lack of true saturation of the instability.
Basepoint free cycles on the moduli space $\overline{M}_{0,n}$ of stable n-pointed rational curves, defined using Gromov-Witten invariants of smooth projective homogeneous spaces X are studied. Intersection formulas to find classes are given, with explicit examples for X a projective space, and X a smooth projective quadric hypersurface. When X is projective space, divisors are shown equivalent to conformal blocks divisors for type A at level one, giving maps from $\overline{M}_{0,n}$ to birational models constructed as GIT quotients, parametrizing configurations of weighted points supported on (generalized) Veronese curves.
We model a long queue of humans by a continuous-space model in which, when a customer moves forward, they stop a random distance behind the previous customer, but do not move at all if their distance behind the previous customer is below a threshold. The latter assumption leads to ``waves" of motion in which only some random number $W$ of customers move. We prove that $\Pr(W > k)$ decreases as order $k^{-1/2}$; in other words, for large $k$ the $k$'th customer moves on average only once every order $k^{1/2}$ service times. A more refined analysis relies on a non-obvious asymptotic relation to the coalescing Brownian motion process; we give a careful outline of such an analysis without attending to all the technical details.
The properties of K-band selected galaxies (K_AB<24) in the z = 3.09 SSA22 protocluster field are studied. 430 galaxies at 2.6 < z_phot < 3.6 are selected as potential protocluster members in a 112 arcmin^2 area based on their photometric redshifts. We find that \approx 20% of the massive galaxies with stellar masses >10^11 M_sun at z_phot \sim 3.1 have colors consistent with those of quiescent galaxies with ages > 0.5 Gyr. This fraction increases to \approx 50% after correcting for unrelated foreground/background objects. We also find that 30% of the massive galaxies are heavily reddened dusty star-forming galaxies. Few such quiescent galaxies at similar redshifts are seen in typical survey fields. An excess surface density of 24\mu m sources at z_phot \sim 3.1 is also observed, implying the presence of dusty star-formation activity in the protocluster. Cross-correlation with the X-ray data indicates that the fraction of K-band selected protocluster galaxies hosting active galactic nuclei (AGN) is also high compared with the field. The sky distribution of the quiescent galaxies, the 24\mu m sources, and the X-ray AGNs show clustering around a density peak of z=3.1 Ly\alpha emitters (LAEs). A significant fraction of the massive galaxies have already become quiescent, while the dusty star-formation is still active in the SSA22 protocluster. These findings indicate that we are witnessing the formation epoch of massive early-type galaxies at the center of predecessors to present-day rich galaxy clusters.
Cosmologies that match in a volume averaged sense need not generally have the same light propagation behaviors. In particular a universe with inhomogeneity may not demonstrate the Friedmann-Robertson-Walker distance-redshift relation even after volume averaging to FRW spacetime. Even the Dyer-Roeder prescription for incorporating inhomogeneity within a universe equivalent to FRW in an angle averaged sense does not guarantee FRW behavior in general. To legitimately use the FRW distance-redshift relation to interpret observations, the physical conditions must match in a line of sight sense (defined herein: most observations do), since light probes the mass distribution or geometry on all length scales.
A simplified model of the tumor angiogenesis can be described by a Keller-Segel equation \cite{FrTe,Le,Pe}. The stability of traveling waves for the one dimensional system has recently been known by \cite{JinLiWa,LiWa}. In this paper we consider the equation on the two dimensional domain $ (x, y) \in   \mathbf R \times {\mathbf S^{\lambda}}$ for a small parameter $\lambda>0$ where $ \mathbf S^{\lambda}$ is the circle of perimeter $\lambda$. Then the equation allows a planar traveling wave solution of invading types. We establish the nonlinear stability of the traveling wave solution if the initial perturbation is sufficiently small in a weighted Sobolev space without a chemical diffusion. When the diffusion is present, we show a linear stability. Lastly, we prove that any solution with our front conditions eventually becomes planar under certain regularity conditions. The key ideas are to use the Cole-Hopf transformation and to apply the Poincar\'{e} inequality to handle with the two dimensional structure.
Most ULXs are believed to be powered by super-Eddington accreting neutron stars and, perhaps, black holes. Above the Eddington rate the disc is expected to thicken and to launch powerful winds through radiation pressure. Winds have been recently discovered in several ULXs. However, it is yet unclear whether the thickening of the disc or the wind variability causes the switch between the classical soft and supersoft states observed in some ULXs. In order to understand such phenomenology and the overall super-Eddington mechanism, we undertook a large (800 ks) observing campaign with XMM-Newton to study NGC 247 ULX-1, which shifts between a supersoft and classical soft ULX state. The new observations show unambiguous evidence of a wind in the form of emission and absorption lines from highly-ionised ionic species, with the latter indicating a mildly-relativistic outflow (-0.17c) in line with the detections in other ULXs. Strong dipping activity is observed in the lightcurve and primarily during the brightest observations, which is typical among soft ULXs, and indicates a close relationship between the accretion rate and the appearance of the dips. The latter is likely due to a thickening of the disc scale-height and the wind as shown by a progressively increasing blueshift in the spectral lines.
We study the characteristics of the galaxy cluster samples expected from the European Space Agency's Euclid satellite and forecast constraints on cosmological parameters describing a variety of cosmological models. The method used in this paper, based on the Fisher Matrix approach, is the same one used to provide the constraints presented in the Euclid Red Book (Laureijs et al.2011). We describe the analytical approach to compute the selection function of the photometric and spectroscopic cluster surveys. Based on the photometric selection function, we forecast the constraints on a number of cosmological parameter sets corresponding to different extensions of the standard LambdaCDM model. The dynamical evolution of dark energy will be constrained to Delta w_0=0.03 and Delta w_a=0.2 with free curvature Omega_k, resulting in a (w_0,w_a) Figure of Merit (FoM) of 291. Including the Planck CMB covariance matrix improves the constraints to Delta w_0=0.02, Delta w_a=0.07 and a FoM=802. The amplitude of primordial non-Gaussianity, parametrised by f_NL, will be constrained to \Delta f_NL ~ 6.6 for the local shape scenario, from Euclid clusters alone. Using only Euclid clusters, the growth factor parameter \gamma, which signals deviations from GR, will be constrained to Delta \gamma=0.02, and the neutrino density parameter to Delta Omega_\nu=0.0013 (or Delta \sum m_\nu=0.01). We emphasise that knowledge of the observable--mass scaling relation will be crucial to constrain cosmological parameters from a cluster catalogue. The Euclid mission will have a clear advantage in this respect, thanks to its imaging and spectroscopic capabilities that will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies. This information will be further complemented by wide-area multi-wavelength external cluster surveys that will already be available when Euclid flies. [Abridged]
The universe time-asymmetry is essentially produced by its low-entropy unstable initial state. Using quanlitative arguments, Paul Davies has demonstrated that the universe expansion may diminish the entropy gap, therefore explaining its low-entropy state, with respect to the maximal possible entropy at any time. This idea is implemented in a qualitative way\thinspace in a simple homogeneous model. Some rough coincidence with observational data are found
We study the shear viscosity in an effective hydrodynamic theory and holographic model where the translational symmetry is broken by massless scalar fields. We identify the shear viscosity, $\eta$, from the coefficient of the shear tensor in the modified constitutive relation, constructed from thermodynamic quantities, fluid velocity and the scalar fields, which break the translational symmetry explicitly. Our construction of constitutive relation is inspired by those derived from the fluid/gravity correspondence in the weakly disordered limit $m/T \ll 1$. We show that the shear viscosity from the constitutive relation deviates from the one obtained from the usual expression, $\eta^\star = -\lim_{\omega\to 0}(1/\omega) \text{Im} G^{R}_{T^{xy}T^{xy}}(\omega,k=0)$, even at the leading order in disorder strength. In a simple holographic model with broken translational symmetry, we show that both $\eta/s$ and ${\eta}^\star/s$ violate the bound of viscosity-entropy ratio for arbitrary disorder strength.
Opals are structures composed of the closed packing of spheres in the size range of nano-to-micro meter. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation between the diffusion coefficient and the termal and electrical conductivity makes possible to estimate the transport coefficients of opal structures. We estimate this changes as function of the neck size and the mean-free path of the carriers. The theory presented is also applicable to the diffusion problem in other periodic structures.
Two-particle rapidity (or pseudorapidity) correlation function $C(y_1, y_2)$ was used in analysing fluctuation of particle density distribution in rapidity in high-energy heavy-ion collisions. In our research, we argue that for a centrality window, some additional correlation may be caused by a centrality span, when the mean two- and single-particle densities over a centrality window are used directly in the calculation , just like $\left<N(y_1, y_2) \right> / \left[\left<N(y_1)\right>\left<N(y_2)\right>\right]$. We concentrate on removing the influence of collision-centrality span on correlation function, and two calculation methods are raised. In one method, correlation coefficients are considered to be the ratios of probabilities (not the particle density). In the other method, a relative multiplicity is introduced to unity the events of different centralities. For testing the methods, {\sc ampt} model is used and a toy granular model is built to simulate the fluctuation of particle density in rapidity.
A theoretical investigation of the possible existence of the chiral polaron formation in graphene is reported. We present an analytical method to calculate the ground-state of the electron-phonon system within the framework of the Lee-Low and Pines theory. On the basis of our model, the influence of electron-optical phonon interaction onto the graphene electronic spectrum is examined. In this paper, we only considered doubly degenerate optical phonon modes of E_2g symmetry near the zone center Gamma. We show analytically that the energy dispersions of both valance and conduction bands of the pristine graphene differ significantly than those obtained through the standard electron self energy calculations due to the electron-phonon interactions. Furthermore, we prove that the degenerate band structure of the graphene promote the chiral polaron formation.