ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, a new version of the interacting model of new agegraphic dark energy (INADE) is proposed and analyzed in detail. The interaction between dark energy and dark matter is reconsidered. The interaction term $Q=bH_0\rho_{\rm de}^\alpha\rho_{\rm dm}^{1-\alpha}$ is adopted, which abandons the Hubble expansion rate $H$ and involves both $\rho_{\rm de}$ and $\rho_{\rm dm}$. Moreover, the new initial condition for the agegraphic dark energy is used, which solves the problem of accommodating baryon matter and radiation in the model. The solution of the model can be given using an iterative algorithm. A concrete example for the calculation of the model is given. Furthermore, the model is constrained by using the combined Planck data (Planck+BAO+SNIa+$H_0$) and the combined WMAP-9 data (WMAP+BAO+SNIa+$H_0$). Three typical cases are considered: (A) $Q=bH_0\rho_{\rm de}$, (B) $Q=bH_0\sqrt{\rho_{\rm de}\rho_{\rm dm}}$, and (C) $Q=bH_0\rho_{\rm dm}$, which correspond to $\alpha=1$, 1/2, and 0, respectively. The departures of the models from the $\Lambda$CDM model are measured by the $\Delta$BIC and $\Delta$AIC values. It is shown that the INADE model is better than the NADE model in the fit, and the INADE(A) model is the best in fitting data among the three cases.
The birth of gravitational wave astronomy was triggered by the first detection of a signal produced by the merger of two compact objects (also known as a compact binary coalescence event). The following detections made by the Earth-based network of advanced interferometers had a significant impact in many fields of science: astrophysics, cosmology, nuclear physics and fundamental physics. However, compact binary coalescence signals are not the only type of gravitational waves potentially detectable by LIGO, Virgo, and KAGRA. An interesting family of still undetected signals, and the ones that are considered in this review, are the so-called continuous waves, paradigmatically exemplified by the gravitational radiation emitted by galactic, fast-spinning isolated neutron stars with a certain degree of asymmetry in their mass distribution. In this work, I will review the status and the latest results from the analyses of advanced detector data, including searches for dark matter signatures.
In this paper we study generalization of the reversal mapping realized by an arbitrary involutory antimorphism $\Theta$. It generalizes the notion of a palindrome into a $\Theta$-palindrome -- a word invariant under $\Theta$. For languages closed under $\Theta$ we give the relation between $\Theta$-palindromic complexity and factor complexity. We generalize the notion of richness to $\Theta$-richness and we prove analogous characterizations of words that are $\Theta$-rich, especially in the case of set of factors invariant under $\Theta$. A criterion for $\Theta$-richness of $\Theta$-episturmian words is given together with other examples of $\Theta$-rich words.
In this article we prove time-global smoothing effects of dispersive pseudodifferential equations with constant coefficient radially symmetric symbols on real rank one symmetric spaces of noncompact type. We also discuss gain of regularities according to decay rates of initial values for the Schroedinger evolution equation. We introduce some isometric operators and reduce the arguments to the well-known Euclidean case. In our proof, Helgason's Fourier transform and the Radon transform as an elliptic Fourier integral operator play crucial roles.
Here we answer a conjecture by Ron Graham about getting finer upper bounds for van der Waerden numbers in the affirmative, but without the application of double induction or combinatorics as applied to sets of integers that contain some van der Waerden number as an element. Rather we obtain the result solely by exploiting certain properties of any integer greater than one that is divisible by another integer. Our mathematical methods are easily accessible by those whose field of specialization lies outside of combinatorial number theory, such as discrete mathematics, elementary number theory or analytic number theory.
In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary driven particle systems such as the open Kawasaki lattice gas and the zero range model. As a measure of time-symmetric dynamical activity we take the difference $(N_1 - N_L)/T$ in the number of particles entering or leaving the system at the left versus the right edge of the system over time $T$. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.
We give some necessary conditions for the existence of a symplectic resolution for quotient singularities. The McKay correspondence is also worked out for these resolutions.
We give an algorithm, with a singly exponential complexity, deciding whether a tropical linear prevariety is a tropical linear variety. The algorithm relies on a criterion to be a tropical linear variety in terms of a duality between the tropical orthogonalization $A^\perp$ and the double tropical orthogonalization $A^{\perp \perp}$ of a subset $A$ of the vector space $({\mathbb R} \cup \{ \infty \})^n$. We also give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.
For a graph $H$ and integer $k\ge1$, let $r(H;k)$ and $r_\ell(H;k)$ denote the $k$-color Ramsey number and list Ramsey number of $H$, respectively. Motivated by the work of Alon, Buci\'c, Kalvari, Kuperwasser and Szab\'o, who initiated the systematic study of list Ramsey numbers of graphs and hypergraphs, and conjectured that $ r(K_{1,n};k)$ and $r_\ell(K_{1,n};k)$ are always equal, we study the $k$-color Ramsey number for double stars $S(n,m)$, where $n\ge m\ge1$. To the best of our knowledge, little is known on the exact value of $r(S(n,m);k)$ when $k\ge3$. A classic result of Erd\H{o}s and Graham from 1975 asserts that $r(T;k)>k(n-1)+1$ for every tree $T$ with $n\ge 1$ edges and $k$ sufficiently large such that $n$ divides $k-1$. Using a folklore double counting argument in set system and the edge chromatic number of complete graphs, we prove that if $k$ is odd and $n$ is sufficiently large compared with $m$ and $k$, then \[ r(S(n,m);k)=kn+m+2.\] This is a step in our effort to determine whether $r(S(n,m);k)$ and $r_\ell(S(n,m);k)$ are always equal, which remains wide open. We also prove that $ r(S^m_n;k)=k(n-1)+m+2$ if $k $ is odd and $n$ is sufficiently large compared with $m$ and $k$, where $1\le m\le n$ and $S^m_n$ is obtained from $K_{1, n}$ by subdividing $m$ edges each exactly once. We end the paper with some observations towards the list Ramsey number for $S(n,m)$ and $S^m_n$.
We present a comprehensive study of a series of recurrent jets that occurred at the periphery of the NOAA active region 12114 on 2014 July 7. These jets were found to share the same source region and exhibited rotational motions as they propagated outward. The multi-wavelength imaging observations made by the AIA and {\it IRIS} telescopes reveal that some of the jets contain cool plasma only, while some others contain not only cool but also hot plasma. The Doppler velocities calculated from the {\it IRIS} spectra show a continuous evolution from blue to red shifts as the jet motions change from upward to downward. Additionally, some jets exhibit opposite Doppler shifts on their both sides, indicative of rotating motions along their axes. The inclination angle and three-dimensional velocity of the largest jet were inferred from the imaging and spectroscopic observations, which show a high consistence with those derived from the stereoscopic analysis using dual-perspective observations by {\it SDO}/AIA and {\it STEREO}-B/EUVI. By relating the jets to the local UV/EUV and full-disk {\it GOES} X-ray emission enhancements, we found that the previous five small-scale jets were triggered by five bright points while the last/largest one was triggered by a C1.6 solar flare. Together with a number of type III radio bursts generated during the jet eruptions as well as a weak CME that was observed in association with the last jet, our observations provide evidences in support of multi-scale magnetic reconnection processes being responsible for the production of jet events.
In 2016, Yuri Zarhin gave formulas for "dividing a point on a hyperelliptic curve by 2." Given a point $P$ on a hyperelliptic curve $\mathcal{C}$, Zarhin gives the Mumford's representation of every degree $g$ divisor $D$ such that $2(D - g \infty) \sim P - \infty$. The aim of this paper is to generalize Zarhin's result to the superelliptic situation; instead of dividing by 2, we divide by $1 - \zeta$. Even though there is no Mumford's representation for superelliptic curves, we give a formula for functions which cut out $D$.
Shape dynamics is an alternative background-independent approach to classical dynamics that implements Leibnizian philosophy and Mach's Principles. It is a formulation of the dynamics of the universe in terms of the intrinsic and relational degrees of freedom which are objectively observable and not properties defined with respect to an external frame of reference. Shape dynamics is not a very old field of study. Although it was already gradually coming alive out of Julian Barbour's early works on Mach's Principle back in the 1980s, it was invigorated by a series of rigorous works in the last decade.   This work is an exhaustive review of the historical and conceptual underpinning of the theory that extends to Leibniz and Newton's philosophy, and the currently established formulation of the theory, together with some of the major results of its cosmological applications. The structure of this work consists of two parts: In the first one we cover the foundations and the formulation of the theory (both the field and particle ontology), and in the second one we study its applications and reflect on the resolution of the problem of the arrow of time. We end our journey by contemplating some recent ideas and prospects for further developing the theory.
We present a detailed abundance analysis, including spectral syntheses, of a very metal-poor ([Fe/H]= -2.7), peculiar main sequence star, HE0024-2523 detected during the course of the Keck Pilot Program. Radial velocities of this star were obtained during four different observing runs over a time span of 1.1 years, and demonstrate that it is clearly a short period spectroscopic binary. An orbital solution was obtained, and orbital parameters were determined with high precision. The rotational velocity was also measured (vsin i=9.7$\pm$1.5 kms); rotation appears likely to be synchronous with the orbit. The abundance analysis and spectral syntheses indicate that the object is a CH star characterized by extreme s-process enrichment, likely due to mass accretion from an evolved companion which has now probably become a white dwarf. The lead (Pb) abundance of HE0024-2523 is very high, the same as that of the recently discovered lead-rich metal-poor star CS 29526-110, [Pb/Fe]=+3.3. The abundance ratio of the heavy-s to light-s elements, as characterized by Pb and Ba, [Pb/Ba]=+1.9, is the highest yet found for any metal-poor star, and is about 0.7 dex higher than that of CS29526-110. On the basis of the measured isotopic ratio of carbon (12C/13C about 6) we argue that the mass donor must have had an original mass of at least 3 Msun. The unusually short period of this CH star suggests that it underwent a past common-envelope phase with its evolved companion. Our results are compared to the latest available models for AGB yields and s-process nucleosynthesis. We also discuss the possible connection between HE0024-2523 the lithium depletion of halo stars, and halo blue straggler formation.
For a smooth projective curve C with genus g >= 2 and a degree 1 line bundle L on C, let M := SU_{C}(r;L) be the moduli space of stable vector bundles of rank r and with the fixed determinant L. In this paper, we study the small rational curves on M and estimate the codimension of the locus of the small rational curves. In particular, we determine all small rational curves when r = 3.
We investigate the role played by subcritical bubbles at the onset of the electroweak phase transition. Treating the configuration modelling the thermal fluctuations around the homogeneous zero configuration of the Higgs field as a stochastic variable, we describe its dynamics by a phenomenological Langevin equation. This approach allows to properly take into account both the effects of the thermal bath on the system: a systematic dyssipative force, which tends to erase out any initial subcritical configuration, and a random stochastic force responsible for the fluctuations. We show that the contribution to the variance $\lgh\phi^2(t)\rg_V$ in a given volume $V$ from any initial subcritical configuration is quickly damped away and that, in the limit of long times, $\lgh\phi^2(t)\rg_V$ approaches its equilibrium value provided by the stochastic force and independent from the viscosity coefficient, as predicted by the fluctuation-dissipation theorem. In agreement with some recent claims, we conclude that thermal fluctuations do not affect the nucleation of critical bubbles at the onset of the electroweak phase transition making electroweak baryogenesis scenarios still a viable possibility to explain the primordial baryon asymmetry in the Universe.
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra A defined on a transformation groupoid given by the action of a group G on a space E. Owing to the fact that G was assumed to be finite it was possible to compute the model in full details. In the present paper we develop the model in the case when G is a noncompact group. It turns out that also in this case the model works well. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model ``collapses'' to the usual quantum mechanics.
It is known that, in string sigma-model metric, the `extreme' fivebrane solution of D=10 supergravity interpolates between D=10 Minkowski spacetime and a supersymmetric $S^3$ compactification to a linear dilaton vacuum. We show here that, in {\it fivebrane} sigma-model metric, the extreme string solution of D=10 supergravity interpolates between Minkowski spacetime and a hitherto unknown supersymmetric $S^7$ compactification of d=10 supergravity to a three-dimensional anti-de Sitter generalization of the linear dilaton vacuum, which may be invariantly characterized in terms of conformal   Killing vectors. The dilaton field diverges near the string core but this divergence may be eliminated by re-interpreting the string solution as the extreme membrane solution of 11-dimensional supergravity. We show that the latter has an analytic extension through a regular degenerate event horizon to an interior region containing a curvature singularity. We obtain analogous results for other extended object solutions of supergravity theories.
We present a near IR photoresponse study of large area multi-walled carbon nanotube/poly(3-hexylthiophene)-block-polystyrene polymer (MWNT/P3HT-b-PS) nanocomposite films for different loading ratio of MWNT into the polymer matrix. We show that the photocurrent strongly depends on the position of the laser spot with maxiumum photocurrent occurring at the metal - film interface. In addition, compared to the pure MWNT film, the photoresponse is much larger in the MWNT/polymer composite films. The time constant for the photoresponse is slow and varies between 0.6 and 1.2 seconds. We explain the photoresponse by Schottky barrier modulation at the metal - film interface.
We report on the observation of collective atomic recoil lasing and superradiant Rayleigh scattering with ultracold and Bose-Einstein condensed atoms in an optical ring cavity. Both phenomena are based on instabilities evoked by the collective interaction of light with cold atomic gases. This publication clarifies the link between the two effects. The observation of superradiant behavior with thermal clouds as hot as several tens of $\mu\textrm{K}$ proves that the phenomena are driven by the cooperative dynamics of the atoms, which is strongly enhanced by the presence of the ring cavity.
We generalise the sum-of-divisors-function $\sigma$ and evenness to the rings of integers of certain algebraic number fields. In particular, we present necessary and sufficient conditions for even Eisenstein integers to be (norm-)perfect based on the work of McDaniel [McD] on Gaussian integers. Furthermore, some results concerning odd norm-perfect Eisenstein integers and the rings of integers of other cyclotomic fields are proven.
Net-Charge fluctuations in a hadron gas are studied using an effective hadronic interaction. The emphasis of this work is to investigate the corrections of hadronic interactions to the charge fluctuations of a non-interacting resonance gas. Several methods, such as loop, density and virial expansions are employed. The calculations are also extended to SU(3) and some resummation schemes are considered. Although the various corrections are sizable individually, they cancel to a large extent. As a consequence we find that charge fluctuations are rather well described by the free resonance gas.
The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report that they yield strong interference in the propagation of the Majorana fermions, which feel gauge-like potential emergent around the fluxes. We examine the transient spin dynamics triggered by a pulsed magnetic field at an edge. In the absence of excited fluxes, the magnetic-field pulse creates the plane wave of the Majorana fermions, which flows in the quantum spin liquid. Although this wave does not accompany the change of local spin moments in bulk, it induces local moments at the side opposite to the edge under the magnetic-field pulse. We observe the spatial modulation of induced spin moments when fluxes are excited in the bulk region. This behavior is more striking than the case of lattice defects. Moreover, we find that, although the amplitude of the spatial change is almost independent of the distance between lattice defects, it is strongly enhanced by increasing the distance for the case of excited fluxes. The difference is understood from the influence on the itinerant Majorana fermions; the lattice defects change the system locally, but flux excitations alter all the transfer integrals on the string connecting them. The present results will provide another route to observing intrinsic flux excitations distinguished from extrinsic effects such as lattice defects.
Possible types of elementary excitations in the symmetric spin-orbital model on the a square lattice are analyzed using a spherically symmetric self-consistent approach. The excitation spectra are calculated. The behavior of the corresponding correlation functions depending on the temperature and parameters of the model is studied. A schematic phase diagram is plotted. It is shown that the thermodynamics of the system is mainly determined by elementary excitations with the entangled spin and orbital degrees of freedom.
In this paper we consider the problem of analytical continuation of solutions to the system of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., the Cauchy problem.
We consider the existence and asymptotics for the fundamental solution of an elliptic operator in nondivergence form, ${\mathcal L}(x,\del_x)=a_{ij}(x)\del_i\del_i$, for $n\geq 3$. We assume that the coefficients have modulus of continuity satisfying the square Dini condition. For fixed $y$, we construct a solution of ${\mathcal L}Z_y(x)=0$ for $0<|x-y|<\e$ with explicit leading order term which is $O(|x-y|^{2-n}e^{I(x,y)})$ as $x\to y$, where $I(x,y)$ is given by an integral and plays an important role for the fundamental solution: if $I(x,y)$ approaches a finite limit as $x\to y$, then we can solve ${\mathcal L}(x,\del_x)F(x,y)=\de(x-y)$, and $F(x,y)$ is asymptotic as $x\to y$ to the fundamental solution for the constant coefficient operator ${\mathcal L}(y,\del_x)$. On the other hand, if $I(x,y)\to -\infty$ as $x\to y$ then the solution $Z_y(x)$ violates the "extended maximum principle" of Gilbarg & Serrin \cite{GS} and is a distributional solution of ${\mathcal L}(x,\del_x)Z_y(x)=0$ for $|x-y|<\e$ although $Z_y$ is not even bounded as $x\to y$.
We study nodal component count of the following Gaussian Laplace eigenfunctions: monochromatic random waves (MRW) on $\mathbb{R}^2$, arithmetic random waves (ARW) on $\mathbb{T}^2$ and random spherical harmonics (RSH) on $\mathbb{S}^2$. Exponential concentration for nodal component count of RSH on $\mathbb{S}^2$ and ARW on $\mathbb{T}^2$ were established by Nazarov-Sodin and Rozenshein respectively. We prove exponential concentration for nodal component count in the following three cases: MRW on growing Euclidean balls in $\mathbb{R}^2$; RSH and ARW on geodesic balls, in $\mathbb{S}^2$ and $\mathbb{T}^2$ respectively, whose radius is slightly larger than the wavelength scale.
Based upon the Smoluchowski equation on curved manifolds three physical observables are considered for the Brownian displacement, namely, geodesic displacement, $s$, Euclidean displacement, $\delta{\bf R}$, and projected displacement $\delta{\bf R}_{\perp}$. The Weingarten-Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle's diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature [J. Stat. Mech. P08006 (2010)]. Furthermore, it is possible to give exact formulae for $\left<\delta{\bf R}\right>$ and $\left<\delta{\bf R}^{2}\right>$ on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes.
In this paper we consider fractional higher-order stochastic differential equations of the form \begin{align*} \left( \mu + c_\alpha \frac{d^\alpha}{d(-t)^\alpha} \right)^\beta X(t) = \mathcal{E}(t) , \quad t\geq 0,\; \mu>0,\; \beta>0,\; \alpha \in (0,1) \cup \mathbb{N} \end{align*} where $\mathcal{E}(t)$ is a Gaussian white noise. We derive stochastic processes satisfying the above equations of which we obtain explicitly the covariance functions and the spectral functions.