ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is usually assumed that the "$t$" parameter in the equations of dynamics can be identified with the indication of the pointer of a clock. Things are not so easy, however. In fact, since the equations of motion can be written in terms of $t$ but also of $t'=f(t)$, $f$ being any well behaved function, each one of those infinite parametric times $t'$ is as good as the Newtonian one to study classical dynamics. Here we show that the relation between the mathematical parametric time $t$ in the equations of dynamics and the physical dynamical time $\sigma$ that is measured with clocks is more complex and subtle than usually assumed. These two times, therefore, must be carefully distinguished since their difference may have significant consequences. Furthermore, we show that not all the dynamical clock-times are necessarily equivalent and that the observational fingerprint of this non-equivalence has the same form as that of the Pioneer anomaly.
After summarizing the relevant observational data, we discuss how a study of flux tube dynamics in the solar convection zone helps us to understand the formation of sunspots. Then we introduce the flux transport dynamo model and assess its success in modelling both the solar cycle and its departures from strictly periodic behaviour.
We investigate high-mobility two-dimensional electron gases in AlGaAs heterostructures by employing Schottky-gate-dependent measurements of the samples' electron density and mobility. Surprisingly, we find that two different sample configurations can be set in situ with mobilities diering by a factor of more than two in a wide range of densities. This observation is discussed in view of charge redistributions between the doping layers and is relevant for the design of future gateable high-mobility electron gases.
In this paper, we show an analogue of Kural, McDonald and Sah's result on Alladi's formula for global function fields. Explicitly, we show that for a global function field $K$, if a set $S$ of prime divisors has a natural density $\delta(S)$ within prime divisors, then $$-\lim_{n\to\infty} \sum_{\substack{1\le \deg D\le n\\ D\in \mathfrak{D}(K,S)}}\frac{\mu(D)}{|D|}=\delta(S),$$ where $\mu(D)$ is the M\"{o}bius function on divisors and $\mathfrak{D}(K,S)$ is the set of all effective distinguishable divisors whose smallest prime factors are in $S$. As applications, we get the analogue of Dawsey's and Sweeting and Woo's results to the Chebotarev Density Theorem for function fields, and the analogue of Alladi's result to the Prime Polynomial Theorem for arithmetic progressions. We also display a connection between the M\"obius function and the Fourier coefficients of modular form associated to elliptic curves. The proof of our main theorem is similar to the approach in Kural et al.'s article.
Using our new 3-D relativistic electromagnetic particle (REMP) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron-positron jet propagating in an unmagnetized ambient electron-positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value. Behind the bow shock in the jet shock strong electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the new technique to calculate emission from electrons based on simulations with a small system. We obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger system generates a jitter/synchrotron spectrum.
Phi meson production in pion-baryon and baryon-baryon interactions near the production threshold is studied in a boson-exchange model. Parameters in this model are either taken from the Bonn model for the nucleon-nucleon potential or determined from the measured phi meson decay width and the experimental data for the reactions $\pi^-p\arr \phi n$ and $pp\arr pp\phi$. The isospin-averaged cross sections for the reactions $\pi N\arr \phi N$, $\pi \Delta \arr \phi N$, $NN\arr NN\phi$, which are needed in transport models to study phi meson production in heavy-ion collisions at subthreshold energies, have been evaluated. For the reactions $N\Delta\arr NN\phi$ and $\Delta\Delta\arr NN\phi$, which become singular when the exchanged pion is on-shell, the Peierls method is used to calculate their cross sections. We find that the cross section for the reaction $\pi N\arr\phi N$ is much larger than the other cross sections.
There is cumulative evidence showing that, for the most massive galaxies, the fraction of disk-like objects compared to those with spheroidal properties increases with redshift. However, this evolution is thus far based on the surface brightness study of these objects. To explore the consistency of this scenario, it is necessary to measure the dynamical status of these galaxies. With this aim we have obtained seeing-limited near-infrared integral field spectra in the H-band for 10 massive galaxies (M_{stellar} >10^{11} h_{70}^-2 M_{Sun}) at z~1.4 with SINFONI at the VLT. Our sample is selected by their stellar mass and EW[OII] > 15 \AA, to secure their kinematic measurements, but without accounting for any morphological or flux criteria a priori. Through this 3D kinematic spectroscopy analysis we find that half (i.e. 50+/-7%) of our galaxies are compatible with being rotationally supported disks, in agreement with previous morphological expectations. This is a factor of approximately two higher than what is observed in the present Universe for objects of the same stellar mass. Strikingly, the majority of our sample of massive galaxies show extended and fairly high rotational velocity maps, implying that massive galaxies acquire rapidly rotational support and hence gravitational equilibrium. Our sample also show evidence for ongoing interactions and mergers. Summarizing, massive galaxies at high-z show a significant diversity and must have continued evolution beyond the fading of stellar populations, to become their present day counterparts.
We prove the existence of time-quasi-periodic solutions of the incompressible Euler equation on the three-dimensional torus $\T^3$, with a small time-quasi-periodic external force. The solutions are perturbations of constant (Diophantine) vector fields, and they are constructed by means of normal forms and KAM techniques for reversible quasilinear PDEs.
We address the issue of unbiased model selection and propose a methodology based on Bayesian inference to extract physical information from kaon photoproduction $p(\gamma,K^+)\Lambda$ data. We use the single-channel Regge-plus-resonance (RPR) framework for $p(\gamma,K^+)\Lambda$ to illustrate the proposed strategy. The Bayesian evidence Z is a quantitative measure for the model's fitness given the world's data. We present a numerical method for performing the multidimensional integrals in the expression for the Bayesian evidence. We use the $p(\gamma,K^+)\Lambda$ data with an invariant energy W > 2.6 GeV in order to constrain the background contributions in the RPR framework with Bayesian inference. Next, the resonance information is extracted from the analysis of differential cross sections, single and double polarization observables. This background and resonance content constitutes the basis of a model which is coined RPR-2011. It is shown that RPR-2011 yields a comprehensive account of the kaon photoproduction data and provides reasonable predictions for $p(e,e' K^+)\Lambda$ observables.
This paper studies topological properties of the lattices of non-crossing partitions of types A and B and of the poset of injective words. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This strengthens the well-known facts that these posets are Cohen-Macaulay. Our results rely on a new poset fiber theorem which turns out to be a useful tool to prove double (homotopy) Cohen-Macaulayness of a poset. Applications to complexes of injective words are also included.
In this paper we develop techniques for determining the dimension of linear systems of divisors based at a collection of general fat points in P^n by partitioning the monomial basis for the vector space of global sections of O(d). The methods we develop can be viewed as extensions of those developed by Dumnicki. We apply these techniques to produce new lower bounds on multi-point Seshadri constants of P^2 and to provide a new proof of a known result confirming the perfect-power cases of Iarrobino's analogue to Nagata's Conjecture in higher dimension.
[abridged] The LMXB 4U 0614+091 is a source of sporadic thermonuclear (type I) X-ray bursts. We find bursts with a wide variety of characteristics in serendipitous wide-field X-ray observations by EURECA/WATCH, RXTE/ASM, BeppoSAX/WFC, HETE-2/FREGATE, INTEGRAL/IBIS/ISGRI, and Swift/BAT, as well as pointed observations by RXTE/PCA and HEXTE. Most of them reach a peak flux of ~15 Crab, but a few only reach a peak flux below a Crab. One of the bursts shows a very strong photospheric radius-expansion phase. This allows us to evaluate the distance to the source: 3.2 kpc. The burst durations are between 10 sec to 5 min. However, after one of the intermediate-duration bursts, a faint tail is seen to at least ~2.4 hours after the start of the burst. One very long burst lasted for several hours. This superburst candidate was followed by a normal type-I burst only 19 days later. This is, to our knowledge, the shortest burst-quench time among the superbursters. A superburst in this system is difficult to reconcile if it accretes at ~1% L_Edd. The intermediate-duration bursts occurred when 4U 0614+091's persistent emission was lowest and calm, and when bursts were infrequent (on average one every month to 3 months). The average burst rate increased significantly after this period. The maximum average burst recurrence rate is once every week to 2 weeks. The burst behaviour may be partly understood if there is at least an appreciable amount of helium present in the accreted material from the donor star. If the system is an ultra-compact X-ray binary with a CO white-dwarf donor, as has been suggested, this is unexpected. If the bursts are powered by helium, we find that the energy production per accumulated mass is about 2.5 times less than expected for pure helium matter.
The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and $(\sqrt{9+8\varepsilon_c}-3)/2$ for the low-dissipation refrigerators, where $\varepsilon_c =T_c/(T_h-T_c)$ is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.
In this paper, using and implementing a new line of sight CMB code, called CMBAns [1], that allows us to modify H(z) for any given feature at any redshift we study the effect of changes in the expansion history of the Universe on the CMB power spectrum. Motivated by the detailed analytical calculations of the effects of the changes in H(z) on ISW plateau and CMB low multipoles, we study two phenomenological parametric form of the expansion history using WMAP data and through MCMC analysis. Our MCMC analysis shows that the standard LCDM cosmological model is consistent with the CMB data allowing the expansion history of the Universe vary around this model at different redshifts. However, our analysis also shows that a decaying dark energy model proposed in [2] has in fact a marginally better fit than the standard cosmological constant model to CMB data. Concordance of our studies here with the previous analysis showing that Baryon Acoustic Oscillation (BAO) and supernovae data (SN Ia) also prefer mildly this decaying dark energy model to LCDM, makes this finding interesting and worth further investigation.
The hitherto unexplored nonlocality of quantum correlations in the information transfer protocol of remote state preparation (RSP) is investigated in terms of a unified nonlocality argument formulated for teleportation as well as for two distinct RSP schemes. The argument differs only in the respective types of local measurements used in each scenario. One of the RSP schemes uses single particle projective measurements, while the other uses joint Bell-basis measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH type inequalities formulated for each of the RSP setups, while being equal to each other, also turn out to be equal to that of the corresponding Bell-CHSH type local realist inequality for teleportation, using the common resource of non-maximally entangled state. This reveals that for such a resource state, the maximum amount of extractable nonlocality of correlations involved in the transfer of information is the same for the standard teleportation protocol and the two RSP schemes considered here, thereby implying that the essential difference between teleportation and remote state preparation lies in the amount of classical information required to be exchanged between parties, and not in the nonlocality of underlying correlations.
WR140 (WC7pd + O5) is often considered to be the archetype of hot, luminous colliding-wind binaries, with strong cyclic high-energy and dust-formation events. The challenge is that this system is quite extreme, with a long period (nearly an integral 7.94 years) and high eccentricity (e = 0.88). Most of the action thus occurs during the relatively short several-month interval of close periastron passage, which in the most recent 2009 January passage occurred during the northern winter months when this summer Cygnus star was least favourably placed in the sky for groundbased observation. To meet this challenge, various multiwavelength campaigns were organized at different sites and from space, mainly within several months of periastron passage 2009. Of particular interest to this workshop was the MONS optical spectroscopic effort, involving both amateur and professional astronomers at the MONS site on Tenerife from 2008 December through 2009 March. I will describe WR140 in terms of the general phenomenon of hot colliding winds and leave the new campaign details to other speakers at this workshop.
We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads.
Entanglement represents an important resource for quantum information processing, but its generation itself requires physical resources that are limited. We propose a scheme for generating a wide class of entangled qudit-type states of optical field modes at sites separated by noisy medium when only weak optical nonlinearities are available at both sites. The protocol is also based on exploiting a weak probe field, transmitted between the sites and used for generation of quantum correlations between two spatially separated field modes. The idea of probabilistic entanglement enhancement by measurement is discussed, and corresponding scheme for measuring the probe field state with linear optics and photodetectors not resolving photon numbers is proposed. It is shown that the protocol is applicable in the case when decoherence, limited efficiency and dark counts of photodetectors, and uncertainty of nonlinear coupling constants are present.
Magnetoelectric interactions in bilayers of magnetostrictive and piezoelectric phases are mediated by mechanical deformation. Here we discuss the theory and companion data for magnetoelectric (ME) coupling at electromechanical resonance (EMR) in a ferrite-lead zirconate titanate (PZT) bilayer. Estimated ME voltage coefficient versus frequency profiles for nickel, cobalt, or lithium ferrite and PZT reveal a giant ME effect at EMR with the highest coupling expected for cobalt ferrite-PZT. Measurements of resonance ME coupling have been carried out on layered and bulk composites of nickel ferrite-PZT. We observe a factor of 40-600 increase in ME voltage coefficient at EMR compared to low frequency values. Theoretical ME voltage coefficients versus frequency profiles are in excellent agreement with data. The resonance ME effect is therefore a novel tool for enhancing the field conversion efficiency in the composites.
The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics.
We prove that the number of overpseudoprimes to base 2 not exceeding x does not exceed x^(3/4)(1+o(1)).
We work in the context of Markovian rough paths associated to a class of uniformly subelliptic Dirichlet forms [25] and prove a better-than-exponential tail estimate for the accummulated local p-variation functional, which has been introduced and studied in [17]. We comment on the significance of these estimates to a range of currently-studied problems, including the recent results of Chevyrev and Lyons in [18].
Effective field theories (EFT) are commonly used to parameterize effects of BSM physics in vector boson scattering (VBS). For Wilson coefficients which are large enough to produce presently observable effects, the validity range of the EFT represents only a fraction of the energy range covered by the LHC, however. In order to shed light on possible extrapolations into the high energy region, a class of UV-complete toy models, with extra SU(2) multiplets of scalars or of fermions with vector-like weak couplings, is considered. By calculating the Wilson coefficients up to energy-dimension eight, and full one-loop contributions to VBS due to the heavy multiplets, the EFT approach, with and without unitarization at high energy, is compared to the perturbative prediction. For high multiplicities, e.g. nonets of fermions, the toy models predict sizable effects in transversely polarized VBS, but only outside the validity range of the EFT. At lower energies, dimension-eight operators are needed for an adequate description of the models, providing another example that dimension-eight can be more important than dimension-six operators. A simplified VBFNLO implementation is used to estimate sensitivity of VBS to such BSM effects at the LHC. Unitarization captures qualitative features of the toy models at high energy but significantly underestimates signal cross sections in the threshold region of the new particles.
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).
1) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to compressive waves but propagation is possible even in the limit of incompressibility, where such disturbances could become dominant. 2) In this context a kinetic theory of space-time is introduced, in which hypothetical constituents of the space-time manifold possess such a rotational degree of freedom (spin). Physical fields (i.e. electromagnetic or gravitational) in such a theory are represented as moments of a statistical distribution of these constituents. The spin wave equation from 1) is treated as a candidate for governing light and metric. Such a theory duplicates to first order Maxwell's equations of electromagnetism, Schrodinger's equation for the electron, and the Lorentz transformations of special relativity. Slight deviations from the classical approach are predicted and should be experimentally verifiable.
Stellar shells are low surface brightness features, created during nearly head-on galaxy mergers from the debris of the tidally disrupted satellite. Here, we investigate the formation and evolution mechanism of shells in six dimensions (3d positions and velocities). We propose a new description in action-angle coordinates which condenses the seemingly complex behaviour of an expanding shell system into a simple picture, and stresses the crucial role of the existence of different stripping episodes in the properties of shells. Based on our findings, we construct a method for constraining the potential of the host galaxy and the average epoch of stripping. The method is applicable even if the shells cannot be identified or isolated from the data, or if the data are heavily contaminated with additional foreground stars. These results open up a new possibility to study the ancient merger that built the Milky Way Galaxy's stellar halo.
We study in this article the cohomological properties of Lagrangian families on projective hyper-K\"ahler manifolds. First, we give a criterion for the vanishing of Abel-Jacobi maps of Lagrangian families. Using this criterion, we show that under a natural condition, if the variation of Hodge structures on the degree $1$ cohomomology of the fibers of the Lagrangian family is maximal, its Abel-Jacobi map is trivial. We also construct Lagrangian families on generalized Kummer varieties whose Abel-Jacobi map is not trivial, showing that our criterion is optimal.