Casimir interaction between two concentric cylinders at nonzero temperature

We study the finite temperature Casimir interaction between two concentric cylinders. When the separation between the cylinders is much smaller than the radii of the cylinders, the asymptotic expansions of the Casimir interaction are derived. Both the low temperature and the high temperature regions are considered. The leading terms are found to agree with the proximity force approximations. The low temperature leading term of the temperature correction is also computed and it is found to be independent of the boundary conditions imposed on the larger cylinder.Comment: 6 pages, 1 figur

Adaptive compressive tomography: a numerical study

We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al. Phys. Rev. Lett. 122, 100404 (2019)], which significantly reduces the number of measurement settings to unambiguously reconstruct any rank-deficient state without any a priori knowledge besides its dimension. We show that both entangled and product bases chosen by our adaptive scheme perform comparably well with recently-known compressed-sensing element-probing measurements, and also beat random measurement bases for low-rank quantum states. We also numerically conjecture asymptotic scaling behaviors for this number as a function of the state rank for our adaptive schemes. These scaling formulas appear to be independent of the Hilbert space dimension. As a natural development, we establish a faster hybrid compressive scheme that first chooses random bases, and later adaptive bases as the scheme progresses. As an epilogue, we reiterate important elements of informational completeness for our adaptive scheme.Comment: 12 pages, 12 figure

Misconduct resistance: the management of restricted drugs in the Western Australian public health service

We employ institutional theory to develop and present a framework – involving institutional drivers, organisational reactions, and outcomes – to examine and further understand misconduct resistance in public sector organisations. This framework is applied to an examination of efforts in the Western Australian public health service to prevent misconduct in the management of restricted drugs. We begin by clarifying a definition of misconduct resistance and then synthesise the extant literature develop a typology and framework of corruption resistance. The second part of the paper is a study in which the framework is applied to an examination of why and how the Western Australian public health service has endeavoured to prevent misconduct in the management of restricted drugs. Top-down imposition of regulations rather than shifts in individual employee attitudes is found. The paper concludes by outlining the potential contributions to theory and practice in approaches to increasing misconduct resistance in public health care organisations

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

Conformal Mappings and Dispersionless Toda hierarchy

Let $\mathfrak{D}$ be the space consists of pairs $(f,g)$, where $f$ is a univalent function on the unit disc with $f(0)=0$, $g$ is a univalent function on the exterior of the unit disc with $g(\infty)=\infty$ and $f'(0)g'(\infty)=1$. In this article, we define the time variables $t_n, n\in \Z$, on $\mathfrak{D}$ which are holomorphic with respect to the natural complex structure on $\mathfrak{D}$ and can serve as local complex coordinates for $\mathfrak{D}$. We show that the evolutions of the pair $(f,g)$ with respect to these time coordinates are governed by the dispersionless Toda hierarchy flows. An explicit tau function is constructed for the dispersionless Toda hierarchy. By restricting $\mathfrak{D}$ to the subspace $\Sigma$ consists of pairs where $f(w)=1/\bar{g(1/\bar{w})}$, we obtain the integrable hierarchy of conformal mappings considered by Wiegmann and Zabrodin \cite{WZ}. Since every $C^1$ homeomorphism $\gamma$ of the unit circle corresponds uniquely to an element $(f,g)$ of $\mathfrak{D}$ under the conformal welding $\gamma=g^{-1}\circ f$, the space $\text{Homeo}_{C}(S^1)$ can be naturally identified as a subspace of $\mathfrak{D}$ characterized by $f(S^1)=g(S^1)$. We show that we can naturally define complexified vector fields \pa_n, n\in \Z on $\text{Homeo}_{C}(S^1)$ so that the evolutions of $(f,g)$ on $\text{Homeo}_{C}(S^1)$ with respect to \pa_n satisfy the dispersionless Toda hierarchy. Finally, we show that there is a similar integrable structure for the Riemann mappings $(f^{-1}, g^{-1})$. Moreover, in the latter case, the time variables are Fourier coefficients of $\gamma$ and $1/\gamma^{-1}$.Comment: 23 pages. This is to replace the previous preprint arXiv:0808.072

Probabilistic combinatorial optimization: Moments, semidefinite programming, and asymptotic bounds

10.1137/S1052623403430610SIAM Journal on Optimization151185-20

The non-monotonic shear-thinning flow of two strongly cohesive concentrated suspensions

The behaviour in simple shear of two concentrated and strongly cohesive mineral suspensions showing highly non-monotonic flow curves is described. Two rheometric test modes were employed, controlled stress and controlled shear-rate. In controlled stress mode the materials showed runaway flow above a yield stress, which, for one of the suspensions, varied substantially in value and seemingly at random from one run to the next, such that the up flow-curve appeared to be quite irreproducible. The down-curve was not though, as neither was the curve obtained in controlled rate mode, which turned out to be triple-valued in the region where runaway flow was seen in controlled rising stress. For this first suspension, the total stress could be decomposed into three parts to a good approximation: a viscous component proportional to a plastic viscosity, a constant isostatic contribution, and a third shear-rate dependent contribution associated with the particulate network which decreased with increasing shear-rate raised to the -7/10th power. In the case of the second suspension, the stress could be decomposed along similar lines, although the strain-rate softening of the solid-phase stress was found to be logarithmic and the irreducible isostatic stress was small. The flow curves are discussed in the light of recent simulations and they conform to a very simple but general rule for non-monotonic behaviour in cohesive suspensions and emulsions, namely that it is caused by strain-rate softening of the solid phase stress.Comment: Revised and corrected version accepted by J. non-Newtonian Fluid Mech., this version 24 pages, 9 Figs inc. graphical abstrac

Finite Temperature Casimir Effect in Randall-Sundrum Models

The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use of, as this turns out to be most convenient. Some comments are made on the related contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear in New J. Phy