8,087 research outputs found
Comments on "State equation for the three-dimensional system of 'collapsing' hard spheres"
A recent paper [I. Klebanov et al. \emph{Mod. Phys. Lett. B} \textbf{22}
(2008) 3153; arXiv:0712.0433] claims that the exact solution of the
Percus-Yevick (PY) integral equation for a system of hard spheres plus a step
potential is obtained. The aim of this paper is to show that Klebanov et al.'s
result is incompatible with the PY equation since it violates two known cases:
the low-density limit and the hard-sphere limit.Comment: 4 pages; v2: title chang
On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids
The energy route to the equation of state of hard-sphere fluids is
ill-defined since the internal energy is just that of an ideal gas and thus it
is independent of density. It is shown that this ambiguity can be avoided by
considering a square-shoulder interaction and taking the limit of vanishing
shoulder width. The resulting hard-sphere equation of state coincides exactly
with the one obtained through the virial route. Therefore, the energy and
virial routes to the equation of state of hard-sphere fluids can be considered
as equivalent.Comment: 2 page
Shell-model phenomenology of low-momentum interactions
The first detailed comparison of the low-momentum interaction V_{low k} with
G matrices is presented. We use overlaps to measure quantitatively the
similarity of shell-model matrix elements for different cutoffs and oscillator
frequencies. Over a wide range, all sets of V_{low k} matrix elements can be
approximately obtained from a universal set by a simple scaling. In an
oscillator mean-field approach, V_{low k} reproduces satisfactorily many
features of the single-particle and single-hole spectra on closed-shell nuclei,
in particular through remarkably good splittings between spin-orbit partners on
top of harmonic oscillator closures. The main deficiencies of pure two-nucleon
interactions are associated with binding energies and with the failure to
ensure magicity for the extruder-intruder closures. Here, calculations
including three-nucleon interactions are most needed. V_{low k} makes it
possible to define directly a meaningful unperturbed monopole Hamiltonian, for
which the inclusion of three-nucleon forces is tractable.Comment: 5 pages, 4 figures, minor additions, to appear as Rapid Comm. in
Phys. Rev.
Effects of electron inertia in collisionless magnetic reconnection
We present a study of collisionless magnetic reconnection within the
framework of full two-fluid MHD for a completely ionized hydrogen plasma,
retaining the effects of the Hall current, electron pressure and electron
inertia. We performed 2.5D simulations using a pseudo-spectral code with no
dissipative effects. We check that the ideal invariants of the problem are
conserved down to round-off errors. Our results show that the change in the
topology of the magnetic field lines is exclusively due to the presence of
electron inertia. The computed reconnection rates remain a fair fraction of the
Alfv\'en velocity, which therefore qualifies as fast reconnection
Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient
As is well known, approximate integral equations for liquids, such as the
hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general
thermodynamically inconsistent in the sense that the macroscopic properties
obtained from the spatial correlation functions depend on the route followed.
In particular, the values of the fourth virial coefficient predicted by
the HNC and PY approximations via the virial route differ from those obtained
via the compressibility route. Despite this, it is shown in this paper that the
value of obtained from the virial route in the HNC theory is exactly
three halves the value obtained from the compressibility route in the PY
theory, irrespective of the interaction potential (whether isotropic or not),
the number of components, and the dimensionality of the system. This simple
relationship is confirmed in one-component systems by analytical results for
the one-dimensional penetrable-square-well model and the three-dimensional
penetrable-sphere model, as well as by numerical results for the
one-dimensional Lennard--Jones model, the one-dimensional Gaussian core model,
and the three-dimensional square-well model.Comment: 8 pages; 4 figures; v2: slight change of title; proof extended to
multicomponent fluid
Are the energy and virial routes to thermodynamics equivalent for hard spheres?
The internal energy of hard spheres (HS) is the same as that of an ideal gas,
so that the energy route to thermodynamics becomes useless. This problem can be
avoided by taking an interaction potential that reduces to the HS one in
certain limits. In this paper the square-shoulder (SS) potential characterized
by a hard-core diameter , a soft-core diameter and a
shoulder height is considered. The SS potential becomes the HS one
if (i) , or (ii) , or (iii)
or (iv) and . The
energy-route equation of state for the HS fluid is obtained in terms of the
radial distribution function for the SS fluid by taking the limits (i) and
(ii). This equation of state is shown to exhibit, in general, an artificial
dependence on the diameter ratio . If furthermore the limit
is taken, the resulting equation of state for HS
coincides with that obtained through the virial route. The necessary and
sufficient condition to get thermodynamic consistency between both routes for
arbitrary is derived.Comment: 10 pages, 4 figures; v2: minor changes; to be published in the
special issue of Molecular Physics dedicated to the Seventh Liblice
Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic,
June 11-16, 2006
How `sticky' are short-range square-well fluids?
The aim of this work is to investigate to what extent the structural
properties of a short-range square-well (SW) fluid of range at a
given packing fraction and reduced temperature can be represented by those of a
sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective
stickiness parameter . Such an equivalence cannot hold for the radial
distribution function since this function has a delta singularity at contact in
the SHS case, while it has a jump discontinuity at in the SW case.
Therefore, the equivalence is explored with the cavity function .
Optimization of the agreement between y_{\sw} and y_{\shs} to first order
in density suggests the choice for . We have performed Monte Carlo (MC)
simulations of the SW fluid for , 1.02, and 1.01 at several
densities and temperatures such that , 0.2, and 0.5. The
resulting cavity functions have been compared with MC data of SHS fluids
obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)].
Although, at given values of and , some local discrepancies
between y_{\sw} and y_{\shs} exist (especially for ), the SW
data converge smoothly toward the SHS values as decreases. The
approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal
energy and structure factor of the SW fluid from those of the SHS fluid. Taking
for y_{\shs} the solution of the Percus--Yevick equation as well as the
rational-function approximation, the radial distribution function of the
SW fluid is theoretically estimated and a good agreement with our MC
simulations is found. Finally, a similar study is carried out for short-range
SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1)
corrected, Fig. 14 redone, to be published in JC
Full-vector analysis of a realistic photonic crystal fiber
We analyze the guiding problem in a realistic photonic crystal fiber using a
novel full-vector modal technique, a biorthogonal modal method based on the
nonselfadjoint character of the electromagnetic propagation in a fiber.
Dispersion curves of guided modes for different fiber structural parameters are
calculated along with the 2D transverse intensity distribution of the
fundamental mode. Our results match those achieved in recent experiments, where
the feasibility of this type of fiber was shown.Comment: 3 figures, submitted to Optics Letter
- …