A normalized solitary wave solution of the Maxwell-Dirac equations

We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

Effect of pressure gradients on the different stages of roughness induced boundary layer transition

The physical mechanisms of roughness-induced transition (RIT) in pressure gradient boundary layers are studied using direct numerical simulations. Recent investigations have examined RIT processes in zero-pressure-gradient boundary layers (Suryanarayanan et al., 2019). The present study uses a vorticity dynamics point of view to examine how these processes are altered by a locally accelerating or decelerating flow that strains the vorticity field and creates a net vorticity flux at the wall. Flow acceleration is imposed on specific streamwise extents of the flow. This provides an understanding about how the fundamental mechanisms in different stages of RIT are affected by pressure gradients. The present results suggest that both lift-up and subsequent amplification of the unsteady perturbations are mitigated by flow acceleration. The effect on lift-up is explained by the compression (i.e. large negative value of the stretching term) of the wall-normal vorticity by negative dv/dy. Consistent with earlier experimental observations on spots and wedges, favorable pressure gradients reduce turbulent wedge spreading and nearly arrest the spreading when sufficiently strong. This result is also explained in terms of vorticity dynamics.     

Dynamics of Skew-Information and Bell’s Inequality Correlations for Two Coupled Dipole Qubits with 2-Photon Transition

International Journal of Theoretical Physics - We consider a dissipative system of two qubits interacting with a cavity field through the degenerate 2-photon transitions. The cavity is initially...     

Wimp searches with gamma rays in the Fermi era: Challenges,methods and results

The launch of the gamma-ray telescope Fermi Large Area Telescope (Fermi-LAT) started a pivotal period in indirect detection of dark matter. By outperforming expectations, for the first time a robust and stringent test of the paradigm of weakly interacting massive particles (WIMPs) is within reach. In this paper, we discuss astrophysical targets for WIMP detection and the challenges they present, review the analysis tools which have been employed to tackle these challenges, and summarize the status of constraints on and the claimed detections in the WIMP parameter space. Methods and results will be discussed in comparison to Imaging Air Cherenkov Telescopes. We also provide an outlook on short term and longer term developments.     

Thermal hazard analysis of inorganic peroxide initiators with varying water concentrations

Journal of Thermal Analysis and Calorimetry - Inorganic peroxide (IP) initiators are widely used as initiators in polymerization reactions. However, if IP initiators are in contact with water due...     

On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II

In this paper an inclined edge cracked short beam specimen subjected to symmetric three-point bend loading was designed and examined for conducting mixed-mode I/II fracture toughness experiments. The aspect ratio (i.e. length to width ratio) and the loading span distance are considered much lower than the other conventional cracked bend beam samples. Crack tip parameters such as stress intensity factors and T-stress were computed numerically for this specimen by several finite element analyses and it was demonstrated that the specimen is able to produce full combinations of mode I and II including pure mode II. The practical capability of the short bend beam specimen was studied experimentally by conducting a set of mixed-mode fracture tests on PolymethylMethacrylate (PMMA) as a well-known model brittle material. The critical stress intensity factors, the direction of fracture kinking and the path of fracture trajectory were investigated both experimentally and theoretically using two stress and strain-based fracture criteria. The fracture toughness of tested PMMA was decreased by moving towards mode II case due to the effect of T-stress on the fracture mechanism of the short bend beam specimen.