208,034 research outputs found
End-to-end distance vector distribution with fixed end orientations for the wormlike chain model
We find exact expressions for the end-to-end distance vector distribution function with fixed end orientations for the wormlike chain model. This function in Fourier-Laplace space adopts the form of infinite continued fractions, which emerges upon exploiting the hierarchical structure of the moment-based expansion. Our results are used to calculate the root-mean-square end displacement in a given direction for a chain with both end orientations fixed. We find that the crossover from rigid to flexible chains is marked by the root-mean-square end displacement slowly losing its angular dependence as the coupling between chain conformation and end orientation wanes. However, the coupling remains strong even for relatively flexible chains, suggesting that the end orientation strongly influences chain conformation for chains that are several persistence lengths long. We then show the behavior of the distribution function by a density plot of the probability as a function of the end-to-end distance vector for a wormlike chain in two dimensions with one end pointed in a fixed direction and the other end free (in its orientation). As we progress from high to low rigidity, the distribution function shifts from being peaked at a location near the full contour length of the chain in the forward direction, corresponding to a straight configuration, to being peaked near zero end separation, as in the Gaussian limit. The function exhibits double peaks in the crossover between these limiting behaviors
Spectrum of Chiral Operators in Strongly Coupled Gauge Theories
We analyze the large spectrum of chiral primary operators of three
dimensional fixed points of the renormalization group. Using the space-time
picture of the fixed points and the correspondence between anti-de Sitter
compactifications and conformal field theories we are able to extract the
dimensions of operators in short superconformal multiplets. We write down some
of these operators in terms of short distance theories flowing to these
non-trivial fixed points in the infrared.Comment: harvmac, 16 pages, one acknowledgement adde
Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem
We show how the Fourier transform of a shape in any number of dimensions can
be simplified using Gauss's law and evaluated explicitly for polygons in two
dimensions, polyhedra three dimensions, etc. We also show how this combination
of Fourier and Gauss can be related to numerous classical problems in physics
and mathematics. Examples include Fraunhofer diffraction patterns, Porods law,
Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use
this approach to provide an alternative derivation of Davis's extension of the
Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure
Vector Bosons in the Randall-Sundrum 2 and Lykken-Randall models and unparticles
Unparticle behavior is shown to be realized in the Randall-Sundrum 2 (RS 2)
and the Lykken-Randall (LR) brane scenarios when brane-localized Standard Model
currents are coupled to a massive vector field living in the five-dimensional
warped background of the RS 2 model. By the AdS/CFT dictionary these
backgrounds exhibit certain properties of the unparticle CFT at large N_c and
strong 't Hooft coupling. Within the RS 2 model we also examine and contrast in
detail the scalar and vector position-space correlators at intermediate and
large distances. Unitarity of brane-to-brane scattering amplitudes is seen to
imply a necessary and sufficient condition on the positivity of the bulk mass,
which leads to the well-known unitarity bound on vector operators in a CFT.Comment: 60 pages, 8 figure
- …