20,401 research outputs found
The Osmotic Coefficient of Rod-like Polyelectrolytes: Computer Simulation, Analytical Theory, and Experiment
The osmotic coefficient of solutions of rod-like polyelectrolytes is
considered by comparing current theoretical treatments and simulations to
recent experimental data. The discussion is restricted to the case of
monovalent counterions and dilute, salt-free solutions. The classical
Poisson-Boltzmann solution of the cell model correctly predicts a strong
decrease in the osmotic coefficient, but upon closer look systematically
overestimates its value. The contribution of ion-ion-correlations are
quantitatively studied by MD simulations and the recently proposed DHHC theory.
However, our comparison with experimental data obtained on synthetic,
stiff-chain polyelectrolytes shows that correlation effects can only partly
explain the discrepancy. A quantitative understanding thus requires theoretical
efforts beyond the restricted primitive model of electrolytes.Comment: 16 pages, 2 figure
New variational and multisymplectic formulations of the Euler-Poincar\'e equation on the Virasoro-Bott group using the inverse map
We derive a new variational principle, leading to a new momentum map and a
new multisymplectic formulation for a family of Euler--Poincar\'e equations
defined on the Virasoro-Bott group, by using the inverse map (also called
`back-to-labels' map). This family contains as special cases the well-known
Korteweg-de Vries, Camassa-Holm, and Hunter-Saxton soliton equations. In the
conclusion section, we sketch opportunities for future work that would apply
the new Clebsch momentum map with -cocycles derived here to investigate a
new type of interplay among nonlinearity, dispersion and noise.Comment: 19 page
On a unified formulation of completely integrable systems
The purpose of this article is to show that a differential
system on which admits a set of independent
conservation laws defined on an open subset , is
essentially equivalent on an open and dense subset of ,
with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \
u^\prime_n=u_n$. The main results are illustrated in the case of two concrete
dynamical systems, namely the three dimensional Lotka-Volterra system, and
respectively the Euler equations from the free rigid body dynamics.Comment: 11 page
Effect of grassâclover forage and whole-wheat feeding on the sensory quality of eggs
BACKGROUND: A sensory panel evaluated the sensory profile of eggs from hens from three experimental systems: (1) an indoor system Ă normal layer diet (InL), (2) a grassâclover forage system Ă normal layer diet (GrL), and (3) a grassâclover forage system Ă whole wheat and oyster shells (GrW).
RESULTS: The taste of the albumen was significantly more âwateryâ and the yolks a darker yellow/orange in the eggs from the GrL and GrW groups. The yolk was darkest from the GrW group. The yolks from the InL and GrW groups had a significantly more âfreshâ, less âanimalâ, âcardboardâ, and âintenseâ aroma than the GrL group. The taste of the yolks from the InL and GrW groups was significantlymore âfreshâ and less âcardboardâ-like compared to the GrL group. The yolks tasted significantly less âsulfurousâ in the GrW group than in the GrL group.
CONCLUSION: The combination of a high feed intake from a grassâclover pasture and the type of feed allocated is an important factor in relation to the sensory quality of eggs. Thus, a less favourable sensory profile of eggs was found from hens on a grassâclover pasture and fed a normal layer diet
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds
For an oriented finite volume hyperbolic 3-manifold M with a fixed spin
structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly
speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to
the representation given by the composition of the lift of the holonomy
representation defined by \eta, and the n-dimensional, irreducible, complex
representation of SL(2,C). In the present work, we focus on two aspects of this
invariant: its asymptotic behavior and its relationship with the complex-length
spectrum of the manifold. Concerning the former, we prove that for suitable
spin structures, log(\tau_n(M; \eta)) grows as -n^2 Vol(M)/4\pi, extending thus
the result obtained by W. Mueller for the compact case. Concerning the latter,
we prove that the sequence {\tau_n(M; \eta)} determines the complex-length
spectrum of the manifold up to complex conjugation
Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions
Understanding dielectric spectra can reveal important information about the
dynamics of solvents and solutes from the dipolar relaxation times down to
electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding
salt ions to a polar solution would result in a reduced dielectric permittivity
that arises from the unexpected tendency of solvent dipoles to align opposite
to the applied field. So far, this effect has escaped an experimental
verification, mainly because of the concomitant appearance of dielectric
saturation from which the Hubbard-Onsager decrement cannot be easily separated.
Here we develop a novel non-equilibrium molecular dynamics simulation approach
to determine this decrement accurately for the first time. Using a
thermodynamic consistent all-atom force field we show that for an aqueous
solution containing sodium chloride around 4.8 Mol/l, this effect accounts for
12\% of the total dielectric permittivity. The dielectric decrement can be
strikingly different if a less accurate force field for the ions is used. Using
the widespread GROMOS parameters, we observe in fact an {\it increment} of the
dielectric permittivity rather than a decrement. We can show that this
increment is caused by ion pairing, introduced by a too low dispersion force,
and clarify the microscopic connection between long-living ion pairs and the
appearance of specific features in the dielectric spectrum of the solution
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