ShantanuT01/DACTYL-Pretraining huggingface dataset:
What should these lectures be? The subject assigned to us is so broad that many books can be written about it. So, in planning these lectures I had several options. One would be to focus on a narrow subset of topics and to cover them in great detail. Such a subset necessarily would be highly personal and useful to a few read- ers at best. Another option would be to give a very shallow overview of the whole field, but then it won't be very much different from a highly compressed version of a university course (which anyone can take if they wish so). So, I decided to be selfish and to prepare these lectures as if I was teaching my own graduate student. Given my research interests, I selected what the student would need to know to be able to discuss science with me and to work on joint research projects. So, the story presented below is both personal and incomplete, but it does cover several subjects that are poorly represented in the existing textbooks (if at all). Some of topics I focus on below are closely connected, others are disjoint, some are just side detours on specific technical questions. There is an overlapping theme, however. Our goal is to follow the cosmic gas from large scales, low densities, (rel- atively) simple physics to progressively smaller scales, higher densities, closer rela- tion to galaxies, and more complex and uncertain physics. So, we (you - the reader, and me - the author) are going to follow a "yellow brick road" from the gas well be- yond any galaxy confines to the actual sites of star formation and stellar feedback. On the way we will stop at some places for a tour and run without looking back through some others. So, the road will be uneven, but I hope that some readers find it useful.
We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional Poisson processes and, when the correlation parameter is equal to zero, the univariate distributions coincide with the ones of the space-time fractional Poisson process in Orsingher and Polito (2012). On the other hand, when we consider the time fractional Poisson process, the multivariate finite dimensional distributions are different from the ones presented for the renewal process in Politi et al. (2011). Another case concerns a class of fractional negative binomial processes.
We study the evolution of the energy gap in a unitary Fermi gas as a function of temperature. To this end we approximate the Fermi gas by the Hubbard lattice Hamiltonian and solve using the dynamical mean-field approximation. We have found that below the critical temperature, Tc, the system is a superfluid and the energy gap is decreasing monotonously. For temperatures above Tc the system is an insulator and the corresponding energy gap is monotonously increasing.
We show that a particular subfunctor of the relative logarithmic Picard functor for families of aligned, log semistable curves over a regular base scheme and smooth over an open dense subscheme of the base is representable by a smooth algebraic space which is slightly more separated than the classical relative Picard functor. We show the existence of its maximal separated quotient and give a new functorial interpretation in terms of logarithmic geometry for the N\'eron model of the relative Picard functor of the smooth locus when we restrict to transversal pull backs from spectra of discrete valuation rings. We also show that aligned degenerations are log cohomologically flat.
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front in the straight part of such a domain and moving into the conical part. We show a dichotomy between blocking and spreading, by proving especially some new Liouville type results on stable solutions of semilinear elliptic equations in the whole space R N. We also show that any spreading solution is a transition front having a global mean speed, which is the unique speed of planar fronts, and that it converges at large time in the conical part of the domain to a well-formed front whose position is approximated by expanding spheres. Moreover, we provide sufficient conditions on the size R of the straight part of the domain and on the opening angle $\alpha$ of the conical part, under which the solution emanating from a planar front is blocked or spreads completely in the conical part. We finally show the openness of the set of parameters (R, $\alpha$) for which the propagation is complete.
We discuss the occurrence of the s-process during the radiative interpulse phase of rotating AGB stars. Due to differential rotation, protons are mixed into C12-rich layers after thermal pulses, in the course of the so called third dredge up episode. We follow the time evolution of key isotope abundances in the relevant layers with a post-processing code which includes time dependant mixing and nucleosynthesis. In rotating AGB models, the mixing persists during the entire interpulse phase due to the steep gradient of angular velocity at the envelope-core interface. As the layers containing protons and C12, which are formed this way, become hotter, a C13-pocket is formed in a natural way. However, in this situation also N14 is formed and spread over the entire C13-pocket. We include the neutron consuming N14(n,p) reaction in our network and determine to what extent it reduces the production of trans-iron elements. We propose that rotation may be responsible for the spread of efficiencies of the C13 neutron source as required by observations.
Muons, as a bulk probe of materials, have been used to study the depth profile of charge carrier kinetics in Si wafers by scanning the muon implantation depth. The photoexcited muon spin spectroscopy technique can optically generate excess carriers in semiconductor wafers, while muons can measure the excess carrier density. As a result, carrier recombination lifetime spectra can be obtained. The depth-dependent lifetime spectra enable us to accurately measure the bulk carrier lifetime and surface recombination velocity by fitting the spectra to a simple 1-dimensional diffusion model. Unlike other traditional lifetime spectroscopy techniques, the bulk and surface recombination properties can be readily de-convoluted in this method. Here, we have applied the technique to study silicon wafers both with and without passivation treatment, and have demonstrated that the model can correctly describe the carrier kinetics in these two cases.
Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the underlying SPD manifold. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly pursuing manifold-manifold transformation matrix of column full-rank. Specifically, by exploiting the Riemannian geometry of the manifold of fixed-rank Positive Semidefinite (PSD) matrices, we present a new solution to reduce optimizing over the space of column full-rank transformation matrices to optimizing on the PSD manifold which has a well-established Riemannian structure. Under this solution, we exploit a new supervised SPD similarity learning technique to learn the transformation by regressing the similarities of selected SPD data pairs to their ground-truth similarities on the target SPD manifold. To optimize the proposed objective function, we further derive an algorithm on the PSD manifold. Evaluations on three visual classification tasks show the advantages of the proposed approach over the existing SPD-based discriminant learning methods.
To partition a sequence of n integers into subsets with prescribed sums is an NP-hard problem in general. In this paper we present an efficient solution for the homogeneous version of this problem; i.e. where the elements in each subset add up to the same sum.
The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SAARs) model, the surface is represented by a twodimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a one-dimensional behavior in this regime. Finally, the universality class of the SAARs model, which has been subject of controversy, has been revisited.
Models for the microstructure evolution during hot rolling are reviewed. The basic macroscopic phenomena related to recrystallization are summarized. Constitutive models based on semi empirical equations are compared to more sophisticated models based on cellular automata, vertex and Monte-Carlo-Potts methods. The applicability of each kind of model approach for online and offline process control in steel industry is discussed. While constitutive models are still state-of-the-art for online process control, mesoscale models with a spatial representation of the microstructure can provide better predictive capabilities at the cost of long computation times. To fill this gap a new approach based on modeling the interaction of an ensemble of multiple grains is outlined and first simulation results are presented. The proposed approach allows the unified modeling of dynamic, static and metadynamic recrystallization as well as grain growth.
We apply the time-dependent variational principle of Balian and V\'en\'eroni to the $ \Phi^4$ theory. An appropriate parametrization for the variational objects allows us to write coupled dynamical equations from which we derive approximations for the two-time correlation functions involving two, three or four field operators.
We quantize the topological $\sigma$-model. The quantum master equation of the Batalin-Vilkovisky formalism $\Delta_\rho \Psi = 0$ appears as a condition which eliminates the exact states from the BRST invariant states $\Psi$ defined by $Q \Psi = 0$. The phase space of the BV formalism is a supermanifold with a specific symplectic structure, called the fermionic K\"ahler manifold.
We study the topology of the matter density field in two dimensional slices, and consider how we can use the amplitude $A$ of the genus for cosmological parameter estimation. Using the latest Horizon Run 4 simulation data, we calculate the genus of the smoothed density field constructed from lightcone mock galaxy catalogs. Information can be extracted from the amplitude of the genus by considering both its redshift evolution and magnitude. The constancy of the genus amplitude with redshift can be used as a standard population, from which we derive constraints on the equation of state of dark energy $w_{\rm de}$ - by measuring $A$ at $z \sim 0.1$ and $z \sim 1$, we can place an order $\Delta w_{\rm de} \sim {\cal O}(15\%)$ constraint on $w_{\rm de}$. By comparing $A$ to its Gaussian expectation value we can potentially derive an additional stringent constraint on the matter density $\Delta \Omega_{\rm mat} \sim 0.01$. We discuss the primary sources of contamination associated with the two measurements - redshift space distortion and shot noise. With accurate knowledge of galaxy bias, we can successfully remove the effect of redshift space distortion, and the combined effect of shot noise and non-linear gravitational evolution is suppressed by smoothing over suitably large scales $R_{\rm G} \ge 15 {\rm Mpc}/h$. Without knowledge of the bias, we discuss how joint measurements of the two and three dimensional genus can be used to constrain the growth factor $\beta = f/b$. The method can be applied optimally to redshift slices of a galaxy distribution generated using the drop-off technique.
We conducted an inter-laboratory study of a metallic glass whose main component is nickel. Two determinations of the mass fractions of the different elements present within the sample were asked to the participants: one at an acceleration voltage of 15 or 20 kV and another one at 5 kV. We compare the mass fractions obtained from wavelength dispersive (WDS) and energy dispersive spectrometries (EDS) and also try to find an influence of the kind of EDS detector and its entrance window, the background subtraction method, the use or not of standards as well as the quantification method. Both means of WDS and EDS mass fractions are close to the reference values. The dispersion of the results was larger at 5 kV than at 15-20 kV owing to the use of the L lines rather than K lines and to the lowest collected intensities. There is an exception with the case of boron because at the lowest voltage, the excitation condition is more favourable for the production of the K line. It appears that the dispersion of the results is larger with EDS than with WDS but it was not possible to find a correlation between the large dispersion and one of the considered experimental parameters and quantification factors. Thus, one can think that electron microprobes are inherently better for the determination of mass fractions or that the implementation of quantitative analysis must be optimized for some cases, especially in SEMs.
We present ab-initio calculations for the in plane conductivity of Co/Cu multilayer slabs. The electronic structure of the multilayer slabs is calculated by means of density functional theory within a screened KKR scheme. Transport properties are described using the Boltzmann equation in relaxation time approximation. We study the change of the conductivity during growth of the multilayer, and we can reproduce the anomalous, non Ohmic, behavior observed experimentally in several multilayer systems. Our results show that this behavior can be explained in terms of the electronic structure of the slab only. No extra assumption for the scattering at the interfaces is necessary. The connection of electronic structure and conductivity during layer-by-layer growth is elucidated by analyzing the layer-projected conductivities.
The short-range nuclear attraction is stronger in the isoscalar channel than in the isovector channel, as evidenced by the existence of the deuteron and not the dineutron. Nevertheless, apart from light N=Z nuclei, pairing is only seen in the isovector channel. This is explained by the effect of the strong spin-orbit splitting on the single-particle energies. A semiquantitative argument is presented treating the high-j orbitals at the Fermi surface as plane waves on a two-dimensional sheet.
In this work, we show that the usage of a quantum gate that gives extra information about the solution searched permits to improve the performance of the search algorithm by switching from quantum to classical search in the appropriated moment. A comparison to the case where only quantum search is used is also realized.
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.
Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum state transformations on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches and will have wide applications.
We present a conformal field theory which desribes a homogeneous four dimensional Lorentz-signature space-time. The model is an ungauged WZW model based on a central extension of the Poincar\'e algebra. The central charge of this theory is exactly four, just like four dimensional Minkowski space. The model can be interpreted as a four dimensional monochromatic plane wave. As there are three commuting isometries, other interesting geometries are expected to emerge via $O(3,3)$ duality.
The widely-used cross-entropy (CE) loss-based deep networks achieved significant progress w.r.t. the classification accuracy. However, the CE loss can essentially ignore the risk of misclassification which is usually measured by the distance between the prediction and label in a semantic hierarchical tree. In this paper, we propose to incorporate the risk-aware inter-class correlation in a discrete optimal transport (DOT) training framework by configuring its ground distance matrix. The ground distance matrix can be pre-defined following a priori of hierarchical semantic risk. Specifically, we define the tree induced error (TIE) on a hierarchical semantic tree and extend it to its increasing function from the optimization perspective. The semantic similarity in each level of a tree is integrated with the information gain. We achieve promising results on several large scale image classification tasks with a semantic tree structure in a plug and play manner.
We develop a hybrid semiclassical method to study the time evolution of one dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time evolving block decimation method, while treating orbital quasiparticle motion classically. We can follow dynamics up to timescales well beyond the reach of standard numerical methods to observe the crossover between pre-equilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel coupled one dimensional Bose condensates. We demonstrate the emergence of soliton-collision induced phase propagation, soliton-entropy production and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.
We show that the valley Chern number of the low energy band in twisted double bilayer graphene can be tuned through two successive topological transitions, where the direct bandgap closes, by changing the electric field perpendicular to the plane of the graphene layers. The two transitions with Chern number changes of -3 and +1 can be explained by the formation of three satellite Dirac points around the central Dirac cone in the moir\'e Brillouin zone due to the presence of trigonal warping. The satellite cones have opposite chirality to the central Dirac cone. Considering the overlap of the bands in energy, which lead to metallic states, we construct the experimentally observable phase diagram of the system in terms of the indirect bandgap and the anomalous valley Hall conductivity. We show that while most of the intermediate phase becomes metallic, there is a narrow parameter regime where the transition through three insulating phases with different quantized valley Hall conductivity can be seen. We systematically study the effects of variations in the model parameters on the phase diagram of the system to reveal the importance of particle-hole asymmetry and trigonal warping in constructing the phase diagram. We also study the effect of changes in interlayer tunneling on this phase diagram.
We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, in ancillary files, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.
The future laser interferometric gravitational-wave detectors sensitivity can be improved using squeezed light. In particular, recently a scheme which uses the optical field with frequency dependent squeeze factor, prepared by means of a relatively short (~30 m) amplitude filter cavity, was proposed \cite{Corbitt2004-3}. Here we consider an improved version of this scheme, which allows to further reduce the quantum noise by exploiting the quantum entanglement between the optical fields at the filter cavity two ports.
In the bilayer quantum Hall coherent state for $\nu_T$ deviating slightly from one, we show that, instead of the global order parameter, the spontaneous breaking of the pseudospin U(1) rotational symmetry is reflected by the periodic domain structure accompanying with the charged meron pairs. The motion of meron pairs induces a novel pseudospin wave. The long range order of the periodic domains in a low bias voltage range leads to the residual zero-bias peak in the tunneling conductance even when the pseudopsin Goldstone feature in a high bias voltage range can be distinct from it.
We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials $\mathcal F^{-1}\left[(b^2 + |\xi|^2)^{-1}\right]$ in 2 dimensions. The authors of \cite{tes2d, geosha} obtained small data scattering and large data global well-posedness in $H^s$ for $s > 0$, respectively. In this paper we show that the small data scattering occurs in $L_x^2(\mathbb R^2)$. This can be done by combining bilinear estimates and modulation estimates of \cite{yang, tes2d}.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting J. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large J and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.