7,047 research outputs found
Aspects of reduction and transformation of Lagrangian systems with symmetry
This paper contains results on geometric Routh reduction and it is a
continuation of a previous paper where a new class of transformations is
introduced between Lagrangian systems obtained after Routh reduction. In
general, these reduced Lagrangian systems have magnetic force terms and are
singular in the sense that the Lagrangian does not depend on some velocity
components. The main purpose of this paper is to show that the Routh reduction
process itself is entirely captured by the application of such a new
transformation on the initial Lagrangian system with symmetry.Comment: To appear in Journal of Geometric Mechanic
Communication: Inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities
A possible approximate route to obtain the equation of state of the
monodisperse hard-sphere system in the metastable fluid region from the
knowledge of the equation of state of a hard-sphere mixture at high densities
is discussed. The proposal is illustrated by using recent Monte Carlo
simulation data for the pressure of a binary mixture. It is further shown to
exhibit high internal consistency.Comment: 4 pages, 2 figures; v2: Simulation data for one-component hard
spheres included in Fig.
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
Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid
The contact values of the radial distribution functions
of a fluid of (additive) hard spheres with a given size distribution
are considered. A ``universality'' assumption is introduced,
according to which, at a given packing fraction ,
, where is a common function
independent of the number of components (either finite or infinite) and
is a
dimensionless parameter, being the -th moment of the diameter
distribution. A cubic form proposal for the -dependence of is made and
known exact consistency conditions for the point particle and equal size
limits, as well as between two different routes to compute the pressure of the
system in the presence of a hard wall, are used to express in terms of
the radial distribution at contact of the one-component system. For
polydisperse systems we compare the contact values of the wall-particle
correlation function and the compressibility factor with those obtained from
recent Monte Carlo simulations.Comment: 9 pages, 7 figure
Evaluation of the potential for dissolved oxygen ingress into deep sedimentary basins during a glaciation event
Geochemical conditions in intracratonic sedimentary basins are currently reducing, even at relatively shallow depths. However, during glaciation-deglaciation events, glacial meltwater production may result in enhanced recharge (Bea et al., 2011; and Bea et al., 2016) potentially having high concentrations of dissolved oxygen (O2). In this study, the reactive transport code Par-MIN3PTHCm was used to perform an informed, illustrative set of simulations assessing the depth of penetration of low salinity, O2-rich, subglacial recharge. Simulation results indicate that the large-scale basin hydrostratigraphy, in combination with the presence of dense brines at depth, results in low groundwater velocities during glacial meltwater infiltration, restricting the vertical ingress of dilute recharge waters. Furthermore, several geochemical attenuation mechanisms exist for O2, which is consumed by reactions with reduced mineral phases and solid organic matter (SOM). The modeling showed that effective oxidative mineral dissolution rates and SOMoxidation rates between 5 × 10-15 and 6 × 10-13 mol dm-3 bulk s-1 were sufficient to restrict the depth of O2 ingress to less than 200m.These effective rates are low and thus conservative, in comparison to rates reported in the literature. Additional simulations with more realistic, yet still conservative, parameters reaffirm the limited ability for O2 to penetrate into sedimentary basin rocks during a glaciation-deglaciation event.Fil: Bea, Sergio Andrés. Universidad Nacional del Centro de la Provincia de Buenos Aires. Rectorado. Instituto de Hidrología de Llanuras - Sede Tandil. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Hidrología de Llanuras - Sede Tandil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Su, Danyang. University of British Columbia; CanadáFil: Mayer, Klaus Ulrich. University of British Columbia; CanadáFil: MacQuarrie, T. B.. University of New Brunswick; Canad
Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal
The contact values of the radial distribution functions
of a -dimensional mixture of (additive) hard spheres are considered. A
`universality' assumption is put forward, according to which
, where is a common function for all
the mixtures of the same dimensionality, regardless of the number of
components, is the packing fraction of the mixture, and is a
dimensionless parameter that depends on the size distribution and the diameters
of spheres and . For , this universality assumption holds for the
contact values of the Percus--Yevick approximation, the Scaled Particle Theory,
and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque
approximation. Known exact consistency conditions are used to express
, , and in terms of the radial distribution
at contact of the one-component system. Two specific proposals consistent with
the above conditions (a quadratic form and a rational form) are made for the
-dependence of . For one-dimensional systems, the proposals for
the contact values reduce to the exact result. Good agreement between the
predictions of the proposals and available numerical results is found for
, 3, 4, and 5.Comment: 10 pages, 11 figures; Figure 1 changed; Figure 5 is new; New
references added; accepted for publication in J. Chem. Phy
Fourth virial coefficients of asymmetric nonadditive hard-disc mixtures
The fourth virial coefficient of asymmetric nonadditive binary mixtures of
hard disks is computed with a standard Monte Carlo method. Wide ranges of size
ratio () and nonadditivity () are
covered. A comparison is made between the numerical results and those that
follow from some theoretical developments. The possible use of these data in
the derivation of new equations of state for these mixtures is illustrated by
considering a rescaled virial expansion truncated to fourth order. The
numerical results obtained using this equation of state are compared with Monte
Carlo simulation data in the case of a size ratio and two
nonadditivities .Comment: 9 pages, 7 figures; v2: section on equation of state added; tables
moved to supplementary material
(http://jcp.aip.org/resource/1/jcpsa6/v136/i18/p184505_s1#artObjSF
Group-Lasso on Splines for Spectrum Cartography
The unceasing demand for continuous situational awareness calls for
innovative and large-scale signal processing algorithms, complemented by
collaborative and adaptive sensing platforms to accomplish the objectives of
layered sensing and control. Towards this goal, the present paper develops a
spline-based approach to field estimation, which relies on a basis expansion
model of the field of interest. The model entails known bases, weighted by
generic functions estimated from the field's noisy samples. A novel field
estimator is developed based on a regularized variational least-squares (LS)
criterion that yields finitely-parameterized (function) estimates spanned by
thin-plate splines. Robustness considerations motivate well the adoption of an
overcomplete set of (possibly overlapping) basis functions, while a sparsifying
regularizer augmenting the LS cost endows the estimator with the ability to
select a few of these bases that ``better'' explain the data. This parsimonious
field representation becomes possible, because the sparsity-aware spline-based
method of this paper induces a group-Lasso estimator for the coefficients of
the thin-plate spline expansions per basis. A distributed algorithm is also
developed to obtain the group-Lasso estimator using a network of wireless
sensors, or, using multiple processors to balance the load of a single
computational unit. The novel spline-based approach is motivated by a spectrum
cartography application, in which a set of sensing cognitive radios collaborate
to estimate the distribution of RF power in space and frequency. Simulated
tests corroborate that the estimated power spectrum density atlas yields the
desired RF state awareness, since the maps reveal spatial locations where idle
frequency bands can be reused for transmission, even when fading and shadowing
effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin
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