29 research outputs found
BIOMECHANICAL LOADING OF THE LOWER EXTREMITIES DURING NORDIC WALKING – A FIELD STUDY
The purpose of this study was to analyse under field conditions the loading of the lower extremities during nordic walking compared to walking. For that purpose 14 experienced, middle aged nordic walkers and 6 nordic walking instructors have been asked to walk a 1575m field track in randomised sequence, once with and once without poles. The mean vertical ground reaction forces are not different between nordic walking and walking. The present results are showing that the common opinion of a load reduction of the lower extremities by 30-50 % during Nordic Walking has to be rejected
Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
The limit n to infinity of the classical O(n) phi^4 model on a 3d film with
free surfaces is studied. Its exact solution involves a self-consistent 1d
Schr\"odinger equation, which is solved numerically for a partially discretized
as well as for a fully discrete lattice model. Numerically exact results are
obtained for the scaled Casimir force at all temperatures. Obtained via a
single framework, they exhibit all relevant qualitative features of the
thermodynamic Casimir force known from wetting experiments on Helium-4 and
Monte Carlo simulations, including a pronounced minimum below the bulk critical
point.Comment: 5 pages, 2 figure
Critical Casimir amplitudes for -component models with O(n)-symmetry breaking quadratic boundary terms
Euclidean -component theories whose Hamiltonians are O(n)
symmetric except for quadratic symmetry breaking boundary terms are studied in
films of thickness . The boundary terms imply the Robin boundary conditions
at the boundary
planes at and . Particular attention is paid
to the cases in which of the variables
take the special value corresponding to critical
enhancement while the remaining ones are subcritically enhanced. Under these
conditions, the semi-infinite system bounded by has a
multicritical point, called -special, at which an symmetric
critical surface phase coexists with the O(n) symmetric bulk phase, provided
is sufficiently large. The -dependent part of the reduced free energy
per area behaves as as at the bulk critical
point. The Casimir amplitudes are determined for small
in the general case where components are
critically enhanced at both boundary planes, components are
enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at
the respective other, and the remaining components satisfy asymptotic
Dirichlet boundary conditions at both . Whenever ,
these expansions involve integer and fractional powers with
(mod logarithms). Results to for general values of
, , and are used to estimate the
of 3D Heisenberg systems with surface spin anisotropies when , , and .Comment: Latex source file with 5 eps files; version with minor amendments and
corrected typo
Thermodynamic Casimir effects involving interacting field theories with zero modes
Systems with an O(n) symmetrical Hamiltonian are considered in a
-dimensional slab geometry of macroscopic lateral extension and finite
thickness that undergo a continuous bulk phase transition in the limit
. The effective forces induced by thermal fluctuations at and above
the bulk critical temperature (thermodynamic Casimir effect) are
investigated below the upper critical dimension by means of
field-theoretic renormalization group methods for the case of periodic and
special-special boundary conditions, where the latter correspond to the
critical enhancement of the surface interactions on both boundary planes. As
shown previously [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero
modes that are present in Landau theory at make conventional
RG-improved perturbation theory in dimensions ill-defined. The
revised expansion introduced there is utilized to compute the scaling functions
of the excess free energy and the Casimir force for temperatures
T\geqT_{c,\infty} as functions of , where
is the bulk correlation length. Scaling functions of the
-dependent residual free energy per area are obtained whose
limits are in conformity with previous results for the Casimir amplitudes
to and display a more reasonable
small- behavior inasmuch as they approach the critical value
monotonically as .Comment: 23 pages, 10 figure
Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
We consider systems confined to a -dimensional slab of macroscopic lateral
extension and finite thickness that undergo a continuous bulk phase
transition in the limit and are describable by an O(n) symmetrical
Hamiltonian. Periodic boundary conditions are applied across the slab. We study
the effects of long-range pair interactions whose potential decays as as , with and , on
the Casimir effect at and near the bulk critical temperature ,
for . For the scaled reduced Casimir force per unit cross-sectional
area, we obtain the form L^{d} {\mathcal F}_C/k_BT \approx \Xi_0(L/\xi_\infty)
+ g_\omega L^{-\omega}\Xi\omega(L/\xi_\infty) + g_\sigma L^{-\omega_\sigm a}
\Xi_\sigma(L \xi_\infty). The contribution decays for
algebraically in rather than exponentially, and hence
becomes dominant in an appropriate regime of temperatures and . We derive
exact results for spherical and Gaussian models which confirm these findings.
In the case , which includes that of nonretarded van-der-Waals
interactions in dimensions, the power laws of the corrections to scaling
of the spherical model are found to get modified by logarithms.
Using general RG ideas, we show that these logarithmic singularities originate
from the degeneracy that occurs for the spherical
model when , in conjunction with the dependence of .Comment: 28 RevTeX pages, 12 eps figures, submitted to PR
Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case
We investigate a two-dimensional Ising model with long-range interactions
that emerge from a generalization of the magnetic dipolar interaction in spin
systems with in-plane spin orientation. This interaction is, in general,
anisotropic whereby in the present work we focus on the isotropic case for
which the model is found to be at its upper critical dimensionality. To
investigate the critical behavior the temperature and field dependence of
several quantities are studied by means of Monte Carlo simulations. On the
basis of the Privman-Fisher hypothesis and results of the renormalization group
the numerical data are analyzed in the framework of a finite-size scaling
analysis and compared to finite-size scaling functions derived from a
Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The
obtained excellent agreement suggests that at least in the present case the
concept of universal finite-size scaling functions can be extended to the upper
critical dimensionality.Comment: revtex4, 10 pages, 5 figures, 1 tabl
Casimir force in O(n) lattice models with a diffuse interface
On the example of the spherical model we study, as a function of the
temperature , the behavior of the Casimir force in O(n) systems with a
diffuse interface and slab geometry , where is
the dimensionality of the system. We consider a system with nearest-neighbor
anisotropic interaction constants parallel to the film and
across it. The model represents the limit of O(n) models
with antiperiodic boundary conditions applied across the finite dimension
of the film. We observe that the Casimir amplitude of the anisotropic -dimensional system is
related to that one of the isotropic system via
. For we find the exact Casimir amplitude , as well as the exact scaling functions of
the Casimir force and of the helicity modulus . We obtain that
, where is the critical temperature of the
bulk system. We find that the effect of the helicity is thus strong that the
Casimir force is repulsive in the whole temperature region.Comment: 15 pages, 3 figure