49,336 research outputs found
Comparison of the oscillatory behaviors of a gravitating Nambu-Goto string with a test string
Comparison of the oscillatory behavior of a gravitating infinite Nambu-Goto
string and a test string is investigated using the general relativistic gauge
invariant perturbation technique with two infinitesimal parameters on a flat
spacetime background. Due to the existence of the pp-wave exact solution, we
see that the conclusion that the dynamical degree of freedom of an infinite
Nambu-Goto string is completely determined by that of gravitational waves,
which was reached in our previous works [K. Nakamura, A. Ishibashi and H.
Ishihara, Phys. Rev. D{\bf 62} (2002), 101502(R); K. Nakamura and H. Ishihara,
Phys. Rev. D{\bf 63} (2001), 127501.], do not contradict to the dynamics of a
test string. We also briefly discuss the implication of this result.Comment: 32 pages, 1 figure, PTPTeX ver.0.8 (LateX2e), Accepted for
publication to Progress of Theoretical Physic
From modes to movement in the behavior of C. elegans
Organisms move through the world by changing their shape, and here we explore
the mapping from shape space to movements in the nematode C. elegans as it
crawls on a planar agar surface. We characterize the statistics of the
trajectories through the correlation functions of the orientation angular
velocity, orientation angle and the mean-squared displacement, and we find that
the loss of orientational memory has significant contributions from both
abrupt, large amplitude turning events and the continuous dynamics between
these events. Further, we demonstrate long-time persistence of orientational
memory in the intervals between abrupt turns. Building on recent work
demonstrating that C. elegans movements are restricted to a low-dimensional
shape space, we construct a map from the dynamics in this shape space to the
trajectory of the worm along the agar. We use this connection to illustrate
that changes in the continuous dynamics reveal subtle differences in movement
strategy that occur among mutants defective in two classes of dopamine
receptors
Morphoelastic rods Part 1: A single growing elastic rod
A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
The spectrum and degeneracies of the Dirac operator are analysed on compact
coset spaces when there is a non-zero homogeneous background gauge field which
is compatible with the symmetries of the space, in particular when the gauge
field is derived from the spin-connection. It is shown how the degeneracy of
the lowest Landau level in the recently proposed higher dimensional quantum
Hall effect is related to the Atiyah-Singer index theorem for the Dirac
operator on a compact coset space.Comment: 25 pages, typeset in LaTeX, uses youngtab.st
The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature
We present the results of a large-scale simulation of a Dynamically
Triangulated Random Surface with extrinsic curvature embedded in
three-dimensional flat space. We measure a variety of local observables and use
a finite size scaling analysis to characterize as much as possible the regime
of crossover from crumpled to smooth surfaces.Comment: 29 pages. There are also 19 figures available from the authors but
not included here - sorr
Black Strings, Black Rings and State-space Manifold
State-space geometry is considered, for diverse three and four parameter
non-spherical horizon rotating black brane configurations, in string theory and
-theory. We have explicitly examined the case of unit Kaluza-Klein momentum
black strings, circular strings, small black rings and black
supertubes. An investigation of the state-space pair correlation functions
shows that there exist two classes of brane statistical configurations, {\it
viz.}, the first category divulges a degenerate intrinsic equilibrium basis,
while the second yields a non-degenerate, curved, intrinsic Riemannian
geometry. Specifically, the solutions with finitely many branes expose that the
two charged rotating black strings and three charged rotating small
black rings consort real degenerate state-space manifolds. Interestingly,
arbitrary valued -dipole charged rotating circular strings and Maldacena
Strominger Witten black rings exhibit non-degenerate, positively curved,
comprehensively regular state-space configurations. Furthermore, the
state-space geometry of single bubbled rings admits a well-defined, positive
definite, everywhere regular and curved intrinsic Riemannian manifold; except
for the two finite values of conserved electric charge. We also discuss the
implication and potential significance of this work for the physics of black
holes in string theory.Comment: 41 pages, Keywords: Rotating Black Branes; Microscopic
Configurations; State-space Geometry, PACS numbers: 04.70.-s Physics of black
holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black
holes, evaporation, thermodynamic
Casimir effect due to a single boundary as a manifestation of the Weyl problem
The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases
the divergences can be eliminated by methods such as zeta-function
regularization or through physical arguments (ultraviolet transparency of the
boundary would provide a cutoff). Using the example of a massless scalar field
theory with a single Dirichlet boundary we explore the relationship between
such approaches, with the goal of better understanding the origin of the
divergences. We are guided by the insight due to Dowker and Kennedy (1978) and
Deutsch and Candelas (1979), that the divergences represent measurable effects
that can be interpreted with the aid of the theory of the asymptotic
distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases
the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having
geometrical origin, and an "intrinsic" term that is independent of the cutoff.
The Weyl terms make a measurable contribution to the physical situation even
when regularization methods succeed in isolating the intrinsic part.
Regularization methods fail when the Weyl terms and intrinsic parts of the
Casimir effect cannot be clearly separated. Specifically, we demonstrate that
the Casimir self-energy of a smooth boundary in two dimensions is a sum of two
Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a
geometrical term that is independent of cutoff, and a non-geometrical intrinsic
term. As by-products we resolve the puzzle of the divergent Casimir force on a
ring and correct the sign of the coefficient of linear tension of the Dirichlet
line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references
added, version to be published in J. Phys.
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