755 research outputs found
Pressure as a Source of Gravity
The active mass density in Einstein's theory of gravitation in the analog of
Poisson's equation in a local inertial system is proportional to .
Here is the density of energy and its pressure for a perfect fluid.
By using exact solutions of Einstein's field equations in the static case we
study whether the pressure term contributes towards the mass
Investigating the trade-off between the effectiveness and efficiency of process modeling
Despite recent efforts to improve the quality of process models, we still observe a significant dissimilarity in quality between models. This paper focuses on the syntactic condition of process models, and how it is achieved. To this end, a dataset of 121 modeling sessions was investigated. By going through each of these sessions step by step, a separate ârevisionâ phase was identified for 81 of them. Next, by cutting the modeling process off at the start of the revision phase, a partial process model was exported for these modeling sessions. Finally, each partial model was compared with its corresponding final model, in terms of time, effort, and the number of syntactic errors made or solved, in search for a possible trade-off between the effectiveness and efficiency of process modeling. Based on the findings, we give a provisional explanation for the difference in syntactic quality of process models
Equation of state for polymer liquid crystals: theory and experiment
The first part of this paper develops a theory for the free energy of
lyotropic polymer nematic liquid crystals. We use a continuum model with
macroscopic elastic moduli for a polymer nematic phase. By evaluating the
partition function, considering only harmonic fluctuations, we derive an
expression for the free energy of the system. We find that the configurational
entropic part of the free energy enhances the effective repulsive interactions
between the chains. This configurational contribution goes as the fourth root
of the direct interactions. Enhancement originates from the coupling between
bending fluctuations and the compressibility of the nematic array normal to the
average director. In the second part of the paper we use osmotic stress to
measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl
solutions. These measurements cover 5 orders of magnitude in DNA osmotic
pressure. At high osmotic pressures the equation of state, dominated by
exponentially decaying hydration repulsion, is independent of the ionic
strength. At lower pressures the equation of state is dominated by fluctuation
enhanced electrostatic double layer repulsion. The measured equation of state
for DNA fits well with our theory for all salt concentrations. We are able to
extract the strength of the direct electrostatic double layer repulsion. This
is a new and alternative way of measuring effective charge densities along
semiflexible polyelectrolytes.Comment: text + 5 figures. Submitted to PR
Quantum Hall Effect in Three Dimensional Layered Systems
Using a mapping of a layered three-dimensional system with significant
inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong
magnetic field limit is obtained in the semi-classical approximation. This
phase diagram, which exhibit a metallic phase for a finite range of energies
and magnetic fields, and the calculated associated critical exponent,
, agree excellently with existing numerical calculations. The
implication of this work for the quantum Hall effect in three dimensions is
discussed.Comment: 4 pages + 4 figure
Theory and Applications of X-ray Standing Waves in Real Crystals
Theoretical aspects of x-ray standing wave method for investigation of the
real structure of crystals are considered in this review paper. Starting from
the general approach of the secondary radiation yield from deformed crystals
this theory is applied to different concreat cases. Various models of deformed
crystals like: bicrystal model, multilayer model, crystals with extended
deformation field are considered in detailes. Peculiarities of x-ray standing
wave behavior in different scattering geometries (Bragg, Laue) are analysed in
detailes. New possibilities to solve the phase problem with x-ray standing wave
method are discussed in the review. General theoretical approaches are
illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table
Non-universal equilibrium crystal shape results from sticky steps
The anisotropic surface free energy, Andreev surface free energy, and
equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a
transfer matrix approach with the density matrix renormalization group (DMRG)
method. The adopted surface model is a restricted solid-on-solid (RSOS) model
with "sticky" steps, i.e., steps with a point-contact type attraction between
them (p-RSOS model). By analyzing the results, we obtain a first-order shape
transition on the ECS profile around the (111) facet; and on the curved surface
near the (001) facet edge, we obtain shape exponents having values different
from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In
order to elucidate the origin of the non-universal shape exponents, we
calculate the slope dependence of the mean step height of "step droplets"
(bound states of steps) using the Monte Carlo method, where p=(dz/dx,
dz/dy)$, and represents the thermal averag |p| dependence of , we
derive a |p|-expanded expression for the non-universal surface free energy
f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order
shape transition and the non-universal shape exponents obtained by the DMRG
calculations are reproduced thermodynamically from the non-universal surface
free energy f_{eff}(p).Comment: 31 pages, 21 figure
Einstein's fluctuation formula. A historical overview
A historical overview is given on the basic results which appeared by the
year 1926 concerning Einstein's fluctuation formula of black-body radiation, in
the context of light-quanta and wave-particle duality. On the basis of the
original publications (from Planck's derivation of the black-body spectrum and
Einstein's introduction of the photons up to the results of Born, Heisenberg
and Jordan on the quantization of a continuum) a comparative study is presented
on the first line of thoughts that led to the concept of quanta. The nature of
the particle-like fluctuations and the wave-like fluctuations are analysed by
using several approaches. With the help of the classical probability theory, it
is shown that the infinite divisibility of the Bose distribution leads to the
new concept of classical poissonian photo-multiplets or to the binary
photo-multiplets of fermionic character. As an application, Einstein's
fluctuation formula is derived as a sum of fermion type fluctuations of the
binary photo-multiplets.Comment: 34 page
Strangeness from 20 AGeV to 158 AGeV
New results from the energy scan programme of NA49, in particular kaon
production at 30 AGeV and phi production at 40 and 80 AGeV are presented. The
K+/pi+ ratio shows a pronounced maximum at 30 AGeV; the kaon slope parameters
are constant at SPS energies. Both findings support the scenario of a phase
transition at about 30 AGeV beam energy. The phi/pi ratio increases smoothly
with beam energy, showing an energy dependence similar to K-/pi-. The measured
particle yields can be reproduced by a hadron gas model, with chemical
freeze-out parameters on a smooth curve in the T-muB plane. The transverse
spectra can be understood as resulting from a rapidly expanding, locally
equilibrated source. No evidence for an earlier kinetic decoupling of heavy
hyperons is found.Comment: Contribution to the proceedings of "Strangeness in Quark Matter 2003"
(March 2003, Atlantic Beach NC, USA), to be published in Journal of Physics
G. 11 pages, 14 figure
Sideward flow of K+ mesons in Ru+Ru and Ni+Ni reactions near threshold
Experimental data on K+ meson and proton sideward flow measured with the FOPI
detector at SIS/GSI in the reactions Ru+Ru at 1.69 AGeV and Ni+Ni at 1.93 AGeV
are presented. The K+ sideward flow is found to be anti-correlated (correlated)
with the one of protons at low (high) transverse momenta. When compared to the
predictions of a transport model, the data favour the existence of an in-medium
repulsive K+ nucleon potential.Comment: 16 pages Revtex, 3 ps-figures, submitted to Phys. Lett.
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is
called Grassmann integral equation in analogy to integral equations studied in
real analysis. A Grassmann integral equation is an equation which involves
Grassmann integrations and which is to be obeyed by an unknown function over a
(finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann
integral equations is explicitly studied for certain low-dimensional Grassmann
algebras. The choice of the equation under investigation is motivated by the
effective action formalism of (lattice) quantum field theory. In a very general
setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional
analogues of the generating functionals of the Green functions are worked out
explicitly by solving a coupled system of nonlinear matrix equations. Finally,
by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi},
{\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the
generators of the Grassmann algebra G_2n), between the finite-dimensional
analogues G_0 and G of the (``classical'') action and effective action
functionals, respectively, a special Grassmann integral equation is being
established and solved which also is equivalent to a coupled system of
nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann
integral equation exist for n=2 (and consequently, also for any even value of
n, specifically, for n=4) but not for n=3. If \lambda=1, the considered
Grassmann integral equation has always a solution which corresponds to a
Gaussian integral, but remarkably in the case n=4 a further solution is found
which corresponds to a non-Gaussian integral. The investigation sheds light on
the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the
reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54],
[61], [64], [139] added
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