5,728 research outputs found
Convexity at finite temperature and non-extensive thermodynamics
Assuming that tunnel effect between two degenerate bare minima occurs, in a
scalar field theory at finite volume, this article studies the consequences for
the effective potential, to all loop orders. Convexity is achieved only if the
two bare minima are taken into account in the path integral, and a new
derivation of the effective potential is given, in the large volume limit. The
effective potential has then has a universal form, it is suppressed by the
space time volume, and does not feature spontaneous symmetry breaking as long
as the volume is finite. The finite temperature analysis leads to surprising
thermal properties, following from the non-extensive expression for the free
energy. Although the physical relevance of these results is not clear, the
potential application to ultra-light scalar particles is discussed.Comment: 17 page
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Optimal exact designs of experiments via Mixed Integer Nonlinear Programming
Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points
Autofocusing and self-healing of partially blocked circular Airy derivative beams
We numerically and experimentally study the autofocusing and self-healing of
partially blocked circular Airy derivative beams (CADBs). The CADB consists of
multiple rings, and partial blocking of CADB with different kinds is achieved
by using symmetric and asymmetric binary amplitude masks, enabling blocking of
inner/outer rings and sectorially. The CADB blocked with different types
possesses the ability to autofocus, however, the required propagation distance
for abrupt autofocusing vary with the amount and types of blocking. The abrupt
autofocusing is quantified by a maximum k-value, and how fast it changes around
the autofocusing distance (). In particular, CADB blocked with inner
rings (first/two/three) exhibits an abrupt autofocusing, as the k-value sharply
increases [decreases] just before [after] . The maximum k-value always
occurs at , which decreases as the number of blocked inner rings
increases. For CADB blocked with outer rings, the k-value gradually changes
around , indicating a lack of abrupt autofocusing. The value of
increases with the number of blocked outer rings. This suggests that
although outer rings contain low intensities, these play an important role in
autofocusing. A sectorially blocked CADB possesses an abrupt autofocusing, and
maximum k-value depends on the amount of blocking. The CADB blocked with
different types possesses good self-healing abilities, where blocked parts
reappear as a result of redistribution of intensity. The maximum self-healing
occurs at , where an overlap integral approaches a maximum value.
Finally, we have compared ideal CADB and partially blocked CADB having the same
radii, and found that an ideal CADB possesses better abrupt autofocusing. We
have found a good agreement between the numerical simulations and experimental
results.Comment: 16 pages, 20 figure
Introducing symplectic billiards
In this article we introduce a simple dynamical system called symplectic
billiards. As opposed to usual/Birkhoff billiards, where length is the
generating function, for symplectic billiards symplectic area is the generating
function. We explore basic properties and exhibit several similarities, but
also differences of symplectic billiards to Birkhoff billiards.Comment: 41 pages, 16 figure
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