ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a three-component reaction-diffusion system yielding an asymptotic logarithmic time-dependence for a moving interface. This is naturally related to a Stefan-problem for which both one-sided Dirichlet-type and von Neumann-type boundary conditions are considered. We integrate the dependence of the interface motion on diffusion and reaction parameters and we observe a change from transport behavior and interface motion \sim t^1/2 to logarithmic behavior \sim ln t as a function of time. We apply our theoretical findings to the propagation of carbon depletion in porous dielectrics exposed to a low temperature plasma. This diffusion saturation is reached after about 1 minute in typical experimental situations of plasma damage in microelectronic fabrication. We predict the general dependencies on porosity and reaction rates.
We investigate effects of the Coulomb force on the nuclear pairing properties by performing the Gogny Hartree-Fock-Bogolyubov calculations for the $N=20$, $28$, $50$, $82$ and $126$ nuclei. The Coulomb force reduces the proton pair energy and the even-odd mass difference by about 25%, except for nuclei at and around the proton shell or subshell closure. We then propose a renormalization scheme via a reduction factor $\gamma_p$ for the proton pairing channel. It is found that a single value of $\gamma_p(=0.90)$ well takes account of the Coulombic effect, for nuclei covering wide range of the mass number and the neutron excess including the nuclei around the shell or subshell closure.
We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.
We study exclusive charmonium production in diffractive deep inelastic scattering and ultra-peripheral heavy-ion collisions within the dipole picture. The mass spectrum and light-front wavefunctions of charmonium are obtained from the basis light-front quantization approach, using the one-gluon exchange interaction plus a confining potential inspired by light-front holography. We apply these light-front wavefunctions to exclusive charmonium production. The resulting cross sections are in reasonable agreement with electron-proton collision data at HERA and ultra-peripheral nucleus collision measurements at RHIC and LHC. The charmonium cross-section has model dependence on the dipole model. We observe that the cross-section ratio of excited states to the ground state has a weaker dependence than the cross-section itself. We suggest that measurements of excited states of heavy quarkonium production in future electron-ion collision experiments will impose rigorous constraints on heavy quarkonium light-front wavefunctions, thus improving our understanding of meson structure, which eventually will help us develop a precise description of the gluon distribution function in the small-$x$ regime.
We study the change of entanglement under general linear transformation of modes in a bosonic system and determine the conditions under which entanglement can be generated under such transformation. As an example we consider the thermal entanglement between the vibrational modes of two coupled oscillators and determine the temperature above which quantum correlations are destroyed by thermal fluctuations.
We discuss the conditions for which the non-equilibrium work relation is valid by means of thermodynamic and microscopic arguments.
A set $S\subset\{1,2,...,n\}$ is called a Sidon set if all the sums $a+b~~(a,b\in S)$ are different. Let $S_n$ be the largest cardinality of the Sidon sets in $\{1,2,...,n\}$. In a former article, the author proved the following asymptotic formula $$\sum_{a\in S,~|S|=S_n}a=\frac{1}{2}n^{3/2}+O(n^{111/80+\varepsilon}),$$ where $\varepsilon>0$ is an arbitrary small constant. In this note, we give an extension of the above formula. We show that $$\sum_{a\in S,~|S|=S_n}a^{\ell}=\frac{1}{\ell+1}n^{\ell+1/2}+O\left(n^{\ell+61/160}\right)$$ for any positive integers $\ell$. Besides, we also consider the asymptotic formulae of other type summations involving Sidon sets. The proofs are established in a more general setting, namely we obtain the asymptotic formulae of the Sidon sets with $t$ elements when $t$ is near the magnitude $n^{1/2}$.
Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for continuous-variable measurement-device-independent quantum key distribution using squeezed states against general coherent attacks. The security analysis is derived based on the entanglement-based scheme considering finite size effect. A version of entropic uncertainty relation is exploited to give a lower bound on the conditional smooth min-entropy by trusting Alice's and Bob's devices. The simulation results indicate that, in the universal composable security framework, the protocol can tolerate 2.5 dB and 6.5 dB channel loss against coherent attacks with direct and reverse reconciliation, respectively.
Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of simple quantum devices in a prepare-measure setting suffers from lack of stability and controllability. This gave rise to a group of quantum protocols that provide randomness certified by classical statistical tests -- Device Independent Quantum Random Number Generators. In this paper we review the most relevant results in this field, which allow the production of almost perfect randomness with help of quantum devices, supplemented with an arbitrary weak source of additional randomness. This is in fact the best one could hope for to achieve, as with no starting randomness (corresponding to no free will in a different concept) even a quantum world would have a fully deterministic description.
We have presented an elegant high energy quantum problem, namely, the full Dirac oscillator under axial magnetic field with its full solution. We have found the energy spectrum which is rich and at the same time has a novel structure. The quantized energy levels show coupling of the oscillator frequency with the Larmor frequency in the 2D surface where the electrons under consideration follow a 2D oscillator. The axis in which magnetic field is pointed, the electrons follow a 1D oscillator. There is also coupling between spin and orbital motion and also a coupling between a resultant effect of orbital and spin motion with Larmor precession.
The development of automatic nutrition diaries, which would allow to keep track objectively of everything we eat, could enable a whole new world of possibilities for people concerned about their nutrition patterns. With this purpose, in this paper we propose the first method for simultaneous food localization and recognition. Our method is based on two main steps, which consist in, first, produce a food activation map on the input image (i.e. heat map of probabilities) for generating bounding boxes proposals and, second, recognize each of the food types or food-related objects present in each bounding box. We demonstrate that our proposal, compared to the most similar problem nowadays - object localization, is able to obtain high precision and reasonable recall levels with only a few bounding boxes. Furthermore, we show that it is applicable to both conventional and egocentric images.
For any periodic function $f:{\mathbb N} \to {\mathbb C}$ with period $q$, we study the Dirichlet series $L(s,f):=\sum_{n\geq 1} f(n)/n^s.$ It is well-known that this admits an analytic continuation to the entire complex plane except at $s=1$, where it has a simple pole with residue $$\rho:= q^{-1}\sum_{1\leq a\leq q} f(a).$$ Thus, the function is analytic at $s=1$ when $\rho=0$ and in this case, we study its non-vanishing using the theory of linear forms in logarithms and Dirichlet $L$-series. In this way, we give new proofs of an old criterion of Okada for the non-vanishing of $L(1,f)$ as well as a classical theorem of Baker, Birch and Wirsing. We also give some new necessary and sufficient conditions for the non-vanishing of $L(1,f)$.
We consider the two-dimensional quasilinear wave equations with quadratic nonlinearities. We introduce a new class of null forms and prove uniform boundedness of the highest order norm of the solution for all time. This class of null forms include several prototypical strong null conditions as special cases. To handle the critical decay near the light cone we inflate the nonlinearity through a new normal form type transformation which is based on a deep cancelation between the tangential and normal derivatives with respect to the light cone. Our proof does not employ the Lorentz boost and can be generalized to systems with multiple speeds.
Very sensitive 21cm HI measurements have been made at several locations around the Local Group galaxy M31 using the Green Bank Telescope (GBT) at an angular resolution of 9.1', with a 5$\sigma$ detection level of $\rm{N_{HI} = 3.9 \times 10^{17}~cm^{-2}}$ for a 30 $\rm{km~s^{-1}}$ line. Most of the HI in a 12 square degree area almost equidistant between M31 and M33 is contained in nine discrete clouds that have a typical size of a few kpc and HI mass of $10^5$ M$_{\odot}$. Their velocities in the Local Group Standard of Rest lie between -100 and +40 $\rm{km~s^{-1}}$, comparable to the systemic velocities of M31 and M33. The clouds appear to be isolated kinematically and spatially from each other. The total HI mass of all nine clouds is $1.4 \times 10^6$ M$_{\odot}$ for an adopted distance of 800 kpc with perhaps another $0.2 \times 10^6$ M$_{\odot}$ in smaller clouds or more diffuse emission. The HI mass of each cloud is typically three orders of magnitude less than the dynamical (virial) mass needed to bind the cloud gravitationally. Although they have the size and HI mass of dwarf galaxies, the clouds are unlikely to be part of the satellite system of the Local Group as they lack stars. To the north of M31, sensitive HI measurements on a coarse grid find emission that may be associated with an extension of the M31 high-velocity cloud population to projected distances of $\sim 100$ kpc. An extension of the M31 high-velocity cloud population at a similar distance to the south, toward M33, is not observed.
We investigate some aspects of Pi-stability of D-branes on Calabi-Yau threefolds in cases where there is a point in moduli space where the grades nearly or completely align. We prove that an example of complete alignment is the case of a collapsed del Pezzo surface. It is shown that there is an open neighbourhood of such a point for which Pi-stability reduces to theta-stability of quiver representations. This should be contrasted to the case of the large radius limit where mu-stability of sheaves cannot be extended out over an open neighbourhood.
We report new imaging polarimetry observations of the Galactic compact HII region K3-50 using CanariCam at the Gran Telescopio Canarias. We use a standard polarimetric analysis technique, first outlined by Aitken, to decompose the observed polarisation images centred at 8.7, 10.3, and 12.5 $\mu$m into the emissive and absorptive components from silicate grains that are aligned with the local magnetic field. These components reveal the spatially-resolved magnetic field structures across the mid-infrared emission area of K3-50. We examine these structures and show that they are consistent with previously observed features and physical models of K3-50, such as the molecular torus and the ionised outflow. We propose a 3D geometry for all the structures seen at different wavelengths. We also compute relevant physical quantities in order to estimate the associated magnetic field strengths that would be implied under various physical assumptions. We compare these results with MHD simulations of protostar formation that predict the magnetic field strength and configuration. We find that the magnetic field may be dynamically important in the innermost 0.2 pc of the molecular torus, but that the torus is more likely to be rotationally-supported against gravity outside this radius. Similarly, magnetic fields are unlikely to dominate the {\em global} physics of the ionised outflow, but they may be important in helping confine the flow near the cavity wall in some locations. Ours is the first application of the Aitken technique to spatially-resolved magnetic field structures in multiple layers along the line of sight, effectively a method of "polarisation tomography."
Adaptive optics systems are essential on all large telescopes where image quality is important. These are complex systems with many design parameters requiring optimisation before good performance can be achieved. The simulation of adaptive optics systems is therefore necessary to categorise the expected performance. This paper describes an adaptive optics simulation platform, developed at Durham University, which can be used to simulate adaptive optics systems on the largest proposed future extremely large telescopes (ELTs) as well as current systems. This platform is modular, object oriented and has the benefit of hardware application acceleration which can be used to improve the simulation performance, essential for ensuring that the run time of a given simulation is acceptable. The simulation platform described here can be highly parallelised using parallelisation techniques suited for adaptive optics simulation, whilst still offering the user complete control while the simulation is running. Results from the simulation of a ground layer adaptive optics system are provided as an example to demonstrate the flexibility of this simulation platform.
The switching speed and the write current required for spin-transfer-torque reversal of spintronic devices such as magnetic tunnel junctions (MTJ) currently hinder their wide implementation into memory and logic devices. This problem is further exacerbated as the dimensions of MTJ nanostructures are scaled down to tens of nanometers in diameter, as higher magnetic anisotropy materials are required to meet thermal stability requirements that demand higher switching current densities. Here, we propose a simple solution to these issues based on synthetic ferrimagnet (SFM) structures. It is commonly assumed that to achieve a given switching delay, the current has to exceed the critical current by a certain factor and so a higher critical current implies a higher switching current. We show that this is not the case for SFM structures which can provide significantly reduced switching delay for a given current density, even though the critical current is increased. This non-intuitive result can be understood from the requirements of angular momentum conservation. We conclude that a 20 nm diameter MTJ incorporating the proposed SFM free layer structure can be switched in tens of picosecond time scales. This remarkable switching speed can be attained by employing current perpendicular magnetic anisotropy materials with experimentally demonstrated exchange coupling strengths.
We propose an approach to realize quantum gates with electron spins localized in a semiconductor that uses double occupancy to advantage. With a fast (non-adiabatic) time control of the tunnelling, the probability of double occupancy is first increased and then brought back exactly to zero. The quantum phase built in this process can be exploited to realize fast quantum operations. We illustrate the idea focusing on the half-swap operation, which is the key two-qubit operation needed to build a CNOT gate.
For positive integers $m$ and $k$, we introduce a family of lattices $\mathcal{C}_{k}^{(m)}$ associated to the Cambrian lattice $\mathcal{C}_{k}$ of the dihedral group $I_{2}(k)$. We show that $\mathcal{C}_{k}^{(m)}$ satisfies some basic properties of a Fuss-Catalan generalization of $\mathcal{C}_{k}$, namely that $\mathcal{C}_{k}^{(1)}=\mathcal{C}_{k}$ and $\bigl\lvert\mathcal{C}_{k}^{(m)}\bigr\rvert=\mbox{Cat}^{(m)}\bigl(I_{2}(k)\bigr)$. Subsequently, we prove some structural and topological properties of these lattices---namely that they are trim and EL-shellable---which were known for $\mathcal{C}_{k}$ before. Remarkably, our construction coincides in the case $k=3$ with the $m$-Tamari lattice of parameter 3 due to Bergeron and Pr{\'e}ville-Ratelle. Eventually, we investigate this construction in the context of other Coxeter groups, in particular we conjecture that the lattice completion of the analogous construction for the symmetric group $\mathfrak{S}_{n}$ and the long cycle $(1\;2\;\ldots\;n)$ is isomorphic to the $m$-Tamari lattice of parameter $n$.
We examine the role of spin twists in the formation of domain walls, often called stripes, by focusing on the spin textures found in the cluster spin glass phases of LaSrCuO and YCaBaCuO. To this end, we derive an analytic expression for the spin distortions produced by a frustrating bond, both near the core region of the bond and in the far field, and then derive an expression for interaction energies between such bonds. We critique our analytical theory by comparison to numerical solutions of this problem and find excellent agreement. By looking at collections of small numbers of such bonds localized in some region of a lattice, we demonstrate the stability of small ``clusters'' of spins, each cluster having its own orientation of its antiferromagnetic order parameter. Then, we display a domain wall corresponding to spin twists between clusters of locally ordered spins showing how spin twists can serve as a mechanism for stripe formation. Since the charges are localized in this model, we emphasize that these domain walls are produced in a situation for which no kinetic energy is present in the problem.
We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.
We study the uncertainties of the determination of the ground-state parameters from Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator $\Pi(\mu)$, which allows one to obtain both the OPE to any order and the spectrum of states. We start with the OPE for $\Pi(\mu)$ and analyze the extraction of the square of the ground-state wave function, $R\propto|\Psi_0(\vec r=0)|^2$, from an SVZ sum rule, setting the mass of the ground state $E_0$ equal to its known value and treating the effective continuum threshold as a fit parameter. We show that in a limited ``fiducial'' range of the Borel parameter there exists a solution for the effective threshold which precisely reproduces the exact $\Pi(\mu)$ for any value of $R$ within the range $0.7 \le R/R_0 \le 1.15$ ($R_0$ is the known exact value). Thus, the value of $R$ extracted from the sum rule is determined to a great extent by the contribution of the hadron continuum. Our main finding is that in the cases where the hadron continuum is not known and is modeled by an effective continuum threshold, the systematic uncertainties of the sum-rule procedure cannot be controlled.
We consider the exclusive $P_{\ell 4}$ decays, $P\to (P_1P_2)_V\ell \nu_{\ell}$, where the subindex $V$ means that the invariant mass of the pseudoscalar pair is taken within a small window around the mass of the vector meson $V$. Pole contributions beyond the dominant $P\to V(\to P_1P_2)\ell\nu_{\ell}$ amplitude of $P_{\ell 4}$ decays are identified, which, in turn, affects the determination of the CKM matrix elements $|V_{qq'}|$. We evaluate the effects of those contributions in the extraction of bottom and charm quark mixings. An application to $B\to (\pi\pi)_{\rho}\ell \nu_{\ell}$ data from Belle collaboration, shows an increase in the extracted value of $|V_{ub}|$ in better agreement with determinations based on $B\to \pi\ell\nu_{\ell}$ decays. The effect of the $\rho$ and $D^*$ pole contributions in the determination of $|V_{cd}|$ from the decay $D\to \pi\pi \ell^- \bar{\nu}_{\ell}$, has been also investigated.
The results of 8-year R-band photopolarimetric data of blazar Mrk 421 collected from February 2008 to May 2016 are presented, along with extensive multiwavelength observations covering from radio to TeV $\gamma$-rays around the flares observed in May 2008, March 2010, and April 2013. The most important results are found in 2013 when the source displayed in the R-band a very high brightness state of $11.29\pm 0.03$ mag ($93.60\pm 1.53$ mJy) on April 10th and a polarization degree of ($11.00\pm0.44$) on May 13th. The analysis of the optical data shows that the polarization variability is due to the superposition of two polarized components that might be produced in two distinct emitting regions. An intranight photopolarimetric variability study carried out over 7 nights after the 2013 April maximum found flux and polarization variations on the nights of April 14, 15, 16 and 19. In addition, the flux shows a minimum variability timescale of $\Delta\,t=$2.34$\pm$0.12 hours, and that the polarization degree presented variations of $\sim$ (1 - 2) in a timescale of $\Delta\,t\sim$ minutes. Also, a detailed analysis of the intranight data shows a coherence length of the large-scale magnetic field of $l_B\simeq$ 0.3 pc which is the same order of magnitude to the distance traveled by the relativistic shocks. This result suggests that there is a connection between the intranight polarimetric variations and spatial changes of the magnetic field. Analysis of the complete R-band data along with the historical optical light curve found for this object shows that Mrk 421 varies with a period of 16.26 $\pm$ 1.78 years.
We present the structural, magnetic, thermodynamic, and transport properties of the two new compounds YbPt$_2$Sn and YbPt$_2$In. X-ray powder diffraction shows that they crystallize in different structure types, the hexagonal ZrPt$_2$Al and the cubic Heusler type, respectively. Despite quite different lattice types, both compounds present very similar magnetic properties: a stable trivalent Yb$^{3+}$, no evidence for a sizeable Kondo interaction, and very weak exchange interactions with a strength below 1K as deduced from specific heat $C(T)$. Broad anomalies in $C(T)$ suggest short range magnetic ordering at about 250mK and 180mK for YbPt$_2$Sn and YbPt$_2$In, respectively. The weak exchange and the low ordering temperature result in a large magnetocaloric effect as deduced from the magnetic field dependence of $C(T)$, making these compounds interesting candidates for magnetic cooling. In addition we found in YbPt$_2$In evidences for a charge density wave transition at about 290K. The occurrence of such transitions within several RET$_2$X compound series (RE = rare earth, T = noble metal, X = In, Sn) is analyzed.