4,148 research outputs found
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
Dissimilar response of plant and soil biota communities to long-term nutrient adition in grasslands
The long-term effect of fertilizers on plant diversity and productivity is well known, but long-term effects on soil biota communities have received relatively little attention. Here, we used an exceptional long-lasting (>40 years) grassland fertilization experiment to investigate the long-term effect of Ca, N, PK, and NPK addition on the productivity and diversity of both vegetation and soil biota. Whereas plant diversity increased by liming and decreased by N and NPK, the diversity of nematodes, collembolans, mites, and enchytraeids increased by N, PK, or NPK. Fertilization with NPK and PK increased plant biomass and biomass of enchytraeids and collembolans. Biomass of nematodes and earthworms increased by liming. Our results suggest that soil diversity might be driven by plant productivity rather than by plant diversity. This may imply that the selection of measures for restoring or conserving plant diversity may decrease soil biota diversity. This needs to be tested in future experiment
Shame and guilt in children: Differential situational antecedents and experiential correlates.
Autoparallels From a New Action Principle
We present a simpler and more powerful version of the recently-discovered
action principle for the motion of a spinless point particle in spacetimes with
curvature and torsion. The surprising feature of the new principle is that an
action involving only the metric can produce an equation of motion with a
torsion force, thus changing geodesics to autoparallels. This additional
torsion force arises from a noncommutativity of variations with parameter
derivatives of the paths due to the closure failure of parallelograms in the
presence of torsionComment: Paper in src. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly
with Netscape under
http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm
Topological Aspect of Knotted Vortex Filaments in Excitable Media
Scroll waves exist ubiquitously in three-dimensional excitable media. It's
rotation center can be regarded as a topological object called vortex filament.
In three-dimensional space, the vortex filaments usually form closed loops, and
even linked and knotted. In this letter, we give a rigorous topological
description of knotted vortex filaments. By using the -mapping
topological current theory, we rewrite the topological current form of the
charge density of vortex filaments and use this topological current we reveal
that the Hopf invariant of vortex filaments is just the sum of the linking and
self-linking numbers of the knotted vortex filaments. We think that the precise
expression of the Hopf invariant may imply a new topological constraint on
knotted vortex filaments.Comment: 4 pages, no figures, Accepted by Chin. Phys. Let
The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation
In linear anisotropic elasticity, the elastic properties of a medium are
described by the fourth rank elasticity tensor C. The decomposition of C into a
partially symmetric tensor M and a partially antisymmetric tensors N is often
used in the literature. An alternative, less well-known decomposition, into the
completely symmetric part S of C plus the reminder A, turns out to be
irreducible under the 3-dimensional general linear group. We show that the
SA-decomposition is unique, irreducible, and preserves the symmetries of the
elasticity tensor. The MN-decomposition fails to have these desirable
properties and is such inferior from a physical point of view. Various
applications of the SA-decomposition are discussed: the Cauchy relations
(vanishing of A), the non-existence of elastic null Lagrangians, the
decomposition of the elastic energy and of the acoustic wave propagation. The
acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The
Cauchy part governs the longitudinal wave propagation. We provide explicit
examples of the effectiveness of the SA-decomposition. A complete class of
anisotropic media is proposed that allows pure polarizations in arbitrary
directions, similarly as in an isotropic medium.Comment: 1 figur
Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor
The lecture explains the geometric basis for the recently-discovered
nonholonomic mapping principle which specifies certain laws of nature in
spacetimes with curvature and torsion from those in flat spacetime, thus
replacing and extending Einstein's equivalence principle. An important
consequence is a new action principle for determining the equation of motion of
a free spinless point particle in such spacetimes. Surprisingly, this equation
contains a torsion force, although the action involves only the metric. This
force changes geodesic into autoparallel trajectories, which are a direct
manifestation of inertia. The geometric origin of the torsion force is a
closure failure of parallelograms. The torsion force changes the covariant
conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm
Conformal Einstein equations and Cartan conformal connection
Necessary and sufficient conditions for a space-time to be conformal to an
Einstein space-time are interpreted in terms of curvature restrictions for the
corresponding Cartan conformal connection
Linear connections with propagating spin-3 field in gravity
We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in
Minkowski spacetime is contained in a general Yang--Mills-like Lagrangian of
metric-affine gravity (MAG), the gauge theory of the general affine group in
the presence of a metric. Due to the geometric character of MAG, this can best
be seen by using Vasiliev's frame formalism for higher-spin gauge fields in
which the spin-3 frame is identified with the tracefree nonmetricity one-form
associated with the shear generators of GL(n,R). Furthermore, for specific
gravitational gauge models in the framework of full nonlinear MAG, exact
solutions are constructed, featuring propagating massless and massive spin-3
fields.Comment: References added. Minor corrections and clarifications. To be
published in Phys. Rev.
Optical Vortices during a Super-Resolution Process in a Metamaterial
We show that a super-resolution process with 100% visibility is characterized
by the formation of a point of phase singularity in free space outside the lens
in the form of a saddle with topological charge equal to -1. The saddle point
is connected to two vortices at the end boundary of the lens, and the two
vortices are in turn connected to another saddle point inside the lens. The
structure saddle-vortices-saddle is topologically stable. The formation of the
saddle point in free space explains also the negative flux of energy present in
a certain region of space outside the lens. The circulation strength of the
power flow can be controlled by varying the position of the object plane with
respect to the lens
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