Spherical model of the Stark effect in external scalar and vector fields

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.

The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.Comment: 22 pages, 6 figure

A scalable FPGA-based architecture for depth estimation in SLAM

The current state of the art of Simultaneous Localisation and Mapping, or SLAM, on low power embedded systems is about sparse localisation and mapping with low resolution results in the name of efficiency. Meanwhile, research in this field has provided many advances for information rich processing and semantic understanding, combined with high computational requirements for real-time processing. This work provides a solution to bridging this gap, in the form of a scalable SLAM-specific architecture for depth estimation for direct semi-dense SLAM. Targeting an off-the-shelf FPGA-SoC this accelerator architecture achieves a rate of more than 60 mapped frames/sec at a resolution of 640×480 achieving performance on par to a highly-optimised parallel implementation on a high-end desktop CPU with an order of magnitude improved power consumption. Furthermore, the developed architecture is combined with our previous work for the task of tracking, to form the first complete accelerator for semi-dense SLAM on FPGAs, establishing the state of the art in the area of embedded low-power systems

Nucleon matrix elements and baryon masses in the Dirac orbital model

Using the expansion of the baryon wave function in a series of products of single quark bispinors (Dirac orbitals), the nonsinglet axial and tensor charges of a nucleon are calculated. The leading term yields $g_A = 1.27$ in good agreement with experiment. Calculation is essentially parameter-free and depends only on the strong coupling constant value $\alpha_s$. The importance of lower Dirac bispinor component, yielding 18% to the wave function normalization is stressed. As a check, the baryon decuplet masses in the formalism of this model are also computed using standard values of the string tension $\sigma$ and the strange quark mass $m_s$; the results being in a good agreement with experiment.Comment: 8 pages, 2 tables; LaTeX2

Qualitative Properties of the Dirac Equation in a Central Potential

The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown to involve a squared Dirac operator for the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle criterion, and a `perturbation' resulting from the potential. One then finds that a potential of Coulomb type in the Dirac equation leads to a potential term in the above second-order equations which is not even infinitesimally form-bounded with respect to the free operator. Moreover, the conditions ensuring essential self-adjointness of the second-order operators in the interacting case are changed with respect to the free case, i.e. they are expressed by a majorization involving the parameter in the Coulomb potential and the angular momentum quantum number. The same methods are applied to the analysis of coupled eigenvalue equations when the anomalous magnetic moment of the electron is not neglected.Comment: 22 pages, plain Tex. In the final version, a section has been added, and the presentation has been improve

Heat capacity anomalies of the molecular crystal 1-fluoro-adamantane at low temperatures

Disorder–disorder phase transitions are rare in nature. Here, we present a comprehensive low-temperature experimental and theoretical study of the heat capacity and vibrational density of states of 1-fluoro-adamantane (C10H15F), an intriguing molecular crystal that presents a continuous disorder–disorder phase transition at T¿=¿180 K and a low-temperature tetragonal phase that exhibits fractional fluorine occupancy. It is shown that fluorine occupancy disorder in the low-T phase of 1-fluoro-adamantane gives rise to the appearance of low-temperature glassy features in the corresponding specific heat (i.e., “boson peak” -BP-) and vibrational density of states. We identify the inflation of low-energy optical modes as the main responsible for the appearance of such glassy heat-capacity features and propose a straightforward correlation between the first localized optical mode and maximum BP temperature for disordered molecular crystals (either occupational or orientational). Thus, the present study provides new physical insights into the possible origins of the BP appearing in disordered materials and expands the set of molecular crystals in which “glassy-like” heat-capacity features have been observed.Peer ReviewedPostprint (published version

On the design of experiments to study extreme field limits

We propose experiments on the collision of high intensity electromagnetic pulses with electron bunches and on the collision of multiple electromagnetic pulses for studying extreme field limits in the nonlinear interaction of electromagnetic waves. The effects of nonlinear QED will be revealed in these laser plasma experiments.Comment: 7 pages, 3 figures, 1 table; 15th Advanced Accelerator Concepts Workshop (AAC 2012), Austin, Texas, 10-15 June, 201

Predicting Visual Overlap of Images Through Interpretable Non-Metric Box Embeddings

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features. This expense is further multiplied when a query image is evaluated against a gallery, e.g. in visual relocalization. While we don't obviate the need for geometric verification, we propose an interpretable image-embedding that cuts the search in scale space to essentially a lookup. Our approach measures the asymmetric relation between two images. The model then learns a scene-specific measure of similarity, from training examples with known 3D visible-surface overlaps. The result is that we can quickly identify, for example, which test image is a close-up version of another, and by what scale factor. Subsequently, local features need only be detected at that scale. We validate our scene-specific model by showing how this embedding yields competitive image-matching results, while being simpler, faster, and also interpretable by humans.Comment: ECCV 202

Linking dynamic phenotyping with metabolite analysis to study natural variation in drought responses of Brachypodium distachyon

Drought is an important environmental stress limiting the productivity of major crops worldwide. Understanding drought tolerance and possible mechanisms for improving drought resistance is therefore a prerequisite to develop drought-tolerant crops that produce significant yields with reduced amounts of water. Brachypodium distachyon (Brachypodium) is a key model species for cereals, forage grasses and energy grasses. In this study, initial screening of a Brachypodium germplasm collection consisting of 138 different ecotypes exposed to progressive drought, highlighted the natural variation in morphology, biomass accumulation and responses to drought stress. A core set of ten ecotypes, classified as being either tolerant, susceptible or intermediate, in response to drought stress, were exposed to mild or severe (respectively 15% and 0% soil water content) drought stress and phenomic parameters linked to growth and colour changes were assessed. When exposed to severe drought stress, phenotypic data and metabolite profiling combined with multivariate analysis revealed a remarkable consistency in separating the selected ecotypes into their different pre-defined drought tolerance groups. Increases in several metabolites, including for the phytohormones jasmonic acid and salicylic acid, and TCA-cycle intermediates, were positively correlated with biomass yield and with reduced yellow pixel counts; suggestive of delayed senescence, both key target traits for crop improvement to drought stress. While metabolite analysis also separated ecotypes into the distinct tolerance groupings after exposure to mild drought stress, similar analysis of the phenotypic data failed to do so, confirming the value of metabolomics to investigate early responses to drought stress. The results highlight the potential of combining the analyses of phenotypic and metabolic responses to identify key mechanisms and markers associated with drought tolerance in both the Brachypodium model plant as well as agronomically important crops

Nonperturbative corrections to the quark self-energy

Nonperturbative self-energy of a bound quark is computed gauge-invariantly in the framework of background perturbation theory. The resulting Delta m^2_q is negative and is a universal function of string tension and current quark mass. The shift of hadron mass squared, M^2, due to Delta m^2_q is negative, large for light quarks, and solves the long-standing problem of Regge intercepts in relativistic quark models.Comment: LaTeX2e, 13 pages, minor differences are don