Casimir forces and vacuum energy

2017 ◽  
Author(s):  
Serge Reynaud ◽  
Astrid Lambrecht
Keyword(s):  
Casimir Force ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Thermal Fluctuations ◽  
Model Systems ◽  
Vacuum Field ◽  
Force Measurements ◽  
Casimir Forces ◽  
Current State ◽  
Field Fluctuations

The Casimir force is an effect of quantum vacuum field fluctuations, with applications in many domains of physics. The ideal expression obtained by Casimir, valid for perfect plane mirrors at zero temperature, has to be modified to take into account the effects of the optical properties of mirrors, thermal fluctuations, and geometry. After a general introduction to the Casimir force and a description of the current state of the art for Casimir force measurements and their comparison with theory, this chapter presents pedagogical treatments of the main features of the theory of Casimir forces for one-dimensional model systems and for mirrors in three-dimensional space.

Vacuum field fluctuations and spontaneous emission in a dielectric slab

1992 ◽  
Vol 436 (1897) ◽  
pp. 373-389 ◽  
Keyword(s):  
Spontaneous Emission ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Field Operator ◽  
Vacuum Field ◽  
Emission Rates ◽  
Dielectric Slab ◽  
Spatial Modes ◽  
Field Fluctuations ◽  
Complete Set

The electromagnetic field is quantized on the basis of the complete set of spatial modes of a plane dielectric slab of arbitrary thickness and refractive index but infinite transverse dimensions, located in otherwise empty three-dimensional space. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position both inside and outside the slab. The source-field operator is derived for emission by atoms inside the slab, in the direction perpendicular to its surfaces. Particular attention is given to the possibility of suppressing spontaneous emission by placing atoms in, or close to, a dielectric slab.

scholarly journals STOCHASTIC QUANTIZATION AND CASIMIR FORCES: PISTONS OF ARBITRARY CROSS SECTION

2012 ◽  
Vol 14 ◽  
pp. 485-495
Author(s):  
PABLO RODRIGUEZ-LOPEZ ◽  
RICARDO BRITO ◽  
RODRIGO SOTO
Keyword(s):  
Cross Section ◽  
Casimir Force ◽  
Thermal Fluctuations ◽  
Arbitrary Cross Section ◽  
Stochastic Quantization ◽  
Casimir Forces ◽  
Asymptotic Expressions ◽  
Arbitrary Geometries ◽  
The Laplace Operator ◽  
The Given

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplace operator in the given geometry. Both quantum and thermal fluctuations were considered. Here we use this method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures, as well as short and long distances are obtained. The case of a piston with triangular cross section is analyzed in detail. The regularization of the divergent stress tensor is described.

THE CORRECTIONS TO THE CASIMIR FORCES FOR CONFIGURATIONS USED IN EXPERIMENTS: THE SPHERICAL LENS ABOVE THE PLANE AND TWO CROSSED CYLINDERS

1996 ◽  
Vol 11 (20) ◽  
pp. 3723-3742 ◽  
Author(s):  
G.L. KLIMCHITSKAYA ◽  
YU. V. PAVLOV
Keyword(s):  
Casimir Force ◽  
Second Order ◽  
Force Measurements ◽  
Casimir Forces ◽  
Spherical Lens ◽  
First Order

A general calculation of the corrections to the Casimir force for configurations used in experiments is presented. These corrections are considered up to the second order with respect to the relative amplitudes of the deviations. It is shown that in the case of long scale deviations the leading correction is the first order one and may be both positive and negative. The relative corrections have estimated values of several tens of percent, so they must be taken into account in precision experiments on Casimir force measurements.

MEASUREMENTS OF THE NORMAL AND SHAPE DEPENDENT CASIMIR FORCES USING AN ATOMIC FORCE MICROSCOPE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 711-721 ◽  
Author(s):  
F. CHEN ◽  
B. W. HARRIS ◽  
A. ROY ◽  
U. MOHIDEEN
Keyword(s):  
Atomic Force Microscope ◽  
Casimir Force ◽  
Experimental Results ◽  
Precision Measurements ◽  
Force Measurements ◽  
Casimir Forces ◽  
Atomic Force ◽  
History Of

The precision instrumental developments and the modern unification theories using compact dimensions have motivated a resurgence in the field of Casimir force measurements. Here, after a brief discussion of the history of Casimir force measurements, the experimental results of Casimir force measurements using an Atomic Force Microscope will be presented. Precision measurements of the normal Casimir force, demonstration of the shape dependent Casimir force and the lateral Casimir force will be presented.

scholarly journals Multi-objective evolutionary method for cargo arrangement in a loading space

2017 ◽  
Vol 44 (4) ◽  
pp. 65-74 ◽  
Author(s):  
Michał Taraska ◽  
Remigiusz Iwańkowicz
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Point Of View ◽  
Acceptable Solution ◽  
Strong Base ◽  
Current Form ◽  
Advantages And Disadvantages ◽  
Current State ◽  
Three Dimensional Space

The paper characterises a class of problems for packing boxes in the container. It presents the current state of knowledge in this area and distinguishes evolutionary algorithms, as the most promising in the search for quasi-optimal loading conditions. The method proposed in the paper focuses on certain criteria important from a practical point of view, which in a formalised manner have not been included so far in the solving-problems models. Apart from the traditional consideration of the problem of three-dimensional space loading maximisation, the proposed method considers the deviation of the loaded container weight centre from its symmetry planes and the availability of packages during unloading. New elements in the described method are: the applied criteria, penalty function, way of coding the container loading state in the evolutionary algorithm and fast crossover and mutations operators dedicated to the adopted coding. It was observed that the evolution in the developed algorithm occurs properly, that is seeking to minimise the criteria. The article also includes a calculation example showing the effect of the method with the discussion of the results indicating the advantages and disadvantages of the proposed solution. The performance of the algorithm has been considered in the context of time necessary to obtain the acceptable solution and quality of the obtained solution. It was found that the algorithm in its current form is a strong base for its further improvement.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Sign in / Sign up

Export Citation Format

Share Document