5,720 research outputs found
Probabilistic combinatorial optimization: Moments, semidefinite programming, and asymptotic bounds
10.1137/S1052623403430610SIAM Journal on Optimization151185-20
Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
Finite temperature Casimir theory of the Dirichlet scalar field is developed,
assuming that there is a conventional Casimir setup in physical space with two
infinitely large plates separated by a gap R and in addition an arbitrary
number q of extra compacified dimensions. As a generalization of earlier
theory, we assume in the first part of the paper that there is a scalar
'refractive index' N filling the whole of the physical space region. After
presenting general expressions for free energy and Casimir forces we focus on
the low temperature case, as this is of main physical interest both for force
measurements and also for issues related to entropy and the Nernst theorem.
Thereafter, in the second part we analyze dispersive properties, assuming for
simplicity q=1, by taking into account dispersion associated with the first
Matsubara frequency only. The medium-induced contribution to the free energy,
and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to
appear in Physica Script
Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming
This paper considers an optimum nonuniform FIR transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique and the local solution is a global minimum
An encryption-decryption framework for validating single-particle imaging
We propose an encryption–decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes’ ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design
Pistons modeled by potentials
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
, we provide a formalism that can be applied to any sufficiently smooth
potential.Comment: 10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In
"Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde",
Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp
31
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics
Origins of ferromagnetism in transition-metal doped Si
We present results of the magnetic, structural and chemical characterizations of Mn<sup>+</sup>-implanted Si displaying <i>n</i>-type semiconducting behavior and ferromagnetic ordering with Curie temperature,T<sub>C</sub> well above room temperature. The temperature-dependent magnetization measured by superconducting quantum device interference (SQUID) from 5 K to 800 K was characterized by three different critical temperatures (T*<sub>C</sub>~45 K, T<sub>C1</sub>~630-650 K and T<sub>C2</sub>~805-825 K). Their origins were investigated using dynamic secondary mass ion spectroscopy (SIMS) and transmission electron microscopy (TEM) techniques, including electron energy loss spectroscopy (EELS), Z-contrast STEM (scanning TEM) imaging and electron diffraction. We provided direct evidences of the presence of a small amount of Fe and Cr impurities which were unintentionally doped into the samples together with the Mn<sup>+</sup> ions, as well as the formation of Mn-rich precipitates embedded in a Mn-poor matrix. The observed T*<sub>C</sub> is attributed to the Mn<sub>4</sub>Si<sub>7</sub> precipitates identified by electron diffraction. Possible origins of and are also discussed. Our findings raise questions regarding the origin of the high ferromagnetism reported in many material systems without a careful chemical analysis
Design of interpolative sigma-delta modulators via semi-indefinite programming
This correspondence considers the optimized design of interpolative sigma delta modulators (SDMs). The first optimization problem is to determine the denominator coefficients. The objective of the optimization problem is to minimize the passband energy of the denominator of the loop filter transfer function (excluding the dc poles) subject to the continuous constraint of this function defined in the frequency domain. The second optimization problem is to determine the numerator coefficients in which the cost function is to minimize the stopband ripple energy of the loop filter subject to the stability condition of the noise transfer function (NTF) and signal transfer function (STF). These two optimization problems are actually quadratic semi-infinite programming (SIP) problems. By employing the dual-parameterization method, global optimal solutions that satisfy the corresponding continuous constraints are guaranteed if the filter length is long enough. The advantages of this formulation are the guarantee of the stability of the transfer functions, applicability to design of rational infinite-impulse-response (IIR) filters without imposing specific filter structures, and the avoidance of iterative design of numerator and denominator coefficients. Our simulation results show that this design yields a significant improvement in the signal-to-noise ratio (SNR) and have a larger stability range, compared with the existing designs
Optimal design of magnitude responses of rational infinite impulse response filters
This correspondence considers a design of magnitude responses of optimal rational infinite impulse response (IIR) filters. The design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters (the error function reflects a ripple square magnitude) is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband, as well as the stability condition. Since the cost function is nonsmooth and nonconvex, while the constraints are continuous, this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem. To address this issue, our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints. Then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method. The solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem. Hence, small transition bandwidth filters can be obtained
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