Mode summation approach to Casimir effect between two objects

In this paper, we explore the TGTG formula from the perspective of mode summation approach. Both scalar fields and electromagnetic fields are considered. In this approach, one has to first solve the equation of motion to find a wave basis for each object. The two T's in the TGTG formula are T-matrices representing the Lippmann-Schwinger T-operators, one for each of the objects. The two G's in the TGTG formula are the translation matrices, relating the wave basis of an object to the wave basis of the other object. After discussing the general theory, we apply the prescription to derive the explicit formulas for the Casimir energies for the sphere-sphere, sphere-plane, cylinder-cylinder and cylinder-plane interactions. First the T-matrices for a plane, a sphere and a cylinder are derived for the following cases: the object is imposed with general Robin boundary conditions; the object is semitransparent; and the object is magnetodielectric. Then the operator approach is used to derive the translation matrices. From these, the explicit TGTG formula for each of the scenarios can be written down. Besides summarizing all the TGTG formulas that have been derived so far, we also provide the TGTG formulas for some scenarios that have not been considered before.Comment: 42 page

An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications

In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst

Electromagnetic Casimir piston in higher dimensional spacetimes

We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the $(4+n)$-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the 4-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the 4-dimensional Minkowski spacetime if $h$ is nonzero.Comment: 22 pages, 4 figure

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure

Scalar Casimir effect between two concentric D-dimensional spheres

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel-Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between D-1 dimensional surfaces close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force. PACS number(s): 03.70.+k, 11.10.Kk, 11.10.Gh, 03.65.GeComment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1207.418

Electronic structure studies of Fe- ZnO nanorods by x-ray absorption fine structure

We report the electronic structure studies of well characterized polycrystalline Zn_{1-x}Fe_xO (x = 0.0, 0.01, 0.03, and 0.05) nanorods synthesized by a co-precipitation method through x-ray absorption fine structure (XAFS). X-ray diffraction (XRD) reveals that Fe doped ZnO crystallizes in a single phase wurtzite structure without any secondary phase. From the XRD pattern, it is observed that peak positions shift towards lower 2\theta value with Fe doping. The change in the peak positions with increase in Fe contents clearly indicates that Fe ions are replacing Zn ions in the ZnO matrix. Linear combination fittings (LCF) at Fe K-edge demonstrate that Fe is in mixed valent state (Fe3+/Fe2+) with a ratio of ~ 7:3 (Fe3+:Fe2+). XAFS data is successfully fitted to wurtzite structure using IFEFFIT and Artemis. The results indicate that Fe substitutes Zn site in the ZnO matrix in tetrahedral symmetry.Comment: 7 pages, 5 figures, 2 tables, regular articl

Post-traumatic stress disorder is associated with a higher rate of polypectomy independent of an increased frequency of colonoscopy in Australian veterans: a retrospective review

Background Post-traumatic stress disorder (PTSD) is associated with extensive physical comorbidities, including lower gastrointestinal symptoms. Diagnostic uncertainty and poor therapeutic responses may result in more frequent colonoscopies than clinically necessary. Polypectomy is standard practice when polyps are identified, and if PTSD is a risk factor for polyp formation, one would expect a higher rate of polyp detection and removal in veterans with PTSD than those without PTSD. Aim To determine the association between PTSD and the rate of colonoscopy and polypectomy in Australian veterans. Methods Diagnostic and therapeutic colonoscopy rates in Australian male Veterans aged >= 50 years were examined by reviewing case records of veterans who accessed Department of Veterans' Affairs funded health services between 1 January 2013 and 31 December 2018. Results A total of 138 471 veterans was included, of whom 28 018 had a diagnosis of PTSD; 56.4% were aged >= 65 years. Twenty-one percent of the entire cohort underwent at least one colonoscopy during the study period. Increased rates of diagnostic colonoscopy and polypectomy were associated with the presence of PTSD across all age brackets. The effect was empirically large as veterans with PTSD experience colonoscopy rates 76-81% greater than those without PTSD. Similarly, veterans with PTSD experienced polypectomy rates 76-81% greater than veterans without PTSD, and this increase persisted when controlling for the increased number of diagnostic colonoscopies they undergo. Conclusion The presence of PTSD has a marked impact on colonoscopy rates in Australian veterans. The increased polypectomy rate independent of increased colonoscopy rate suggests that PTSD is a risk factor for colonic polyp formation

Local Structure of La1-xSrxCoO3 determined from EXAFS and neutron PDF studies

The combined local structure techniques, extended x-ray absorption fine structure (EXAFS) and neutron pair distribution function analysis, have been used for temperatures 4 <= T <= 330 K to rule out a large Jahn-Teller (JT) distortion of the Co-O bond in La1-xSrxCoO3 for a significant fraction of Co sites (x <= 0.35), indicating few, if any, JT-active, singly occupied e_g Co sites exist.Comment: 5 page

Structure of Extremely Nanosized and Confined In-O Species in Ordered Porous Materials

Perturbed-angular correlation, x-ray absorption, and small-angle x-ray scattering spectroscopies were suitably combined to elucidate the local structure of highly diluted and dispersed InOx species confined in porous of ZSM5 zeolite. These novel approach allow us to determined the structure of extremely nanosized In-O species exchanged inside the 10-atom-ring channel of the zeolite, and to quantify the amount of In2O3 crystallites deposited onto the external zeolite surface.Comment: 4 pages, 5 postscript figures, REVTEX4, published in Physical Review Letter

Topological Defects and Gapless Modes in Insulators and Superconductors

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified, and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions and helical Majorana fermions, as well as zero dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.Comment: 27 pages, 15 figures, Published versio