5,940 research outputs found
Strongly nonlinear waves in capillary electrophoresis
In capillary electrophoresis, sample ions migrate along a micro-capillary
filled with a background electrolyte under the influence of an applied electric
field. If the sample concentration is sufficiently high, the electrical
conductivity in the sample zone could differ significantly from the
background.Under such conditions, the local migration velocity of sample ions
becomes concentration dependent resulting in a nonlinear wave that exhibits
shock like features. If the nonlinearity is weak, the sample concentration
profile, under certain simplifying assumptions, can be shown to obey Burgers'
equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which
has an exact analytical solution for arbitrary initial condition.In this paper,
we use a numerical method to study the problem in the more general case where
the sample concentration is not small in comparison to the concentration of
background ions. In the case of low concentrations, the numerical results agree
with the weakly nonlinear theory presented earlier, but at high concentrations,
the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material
Reynolds number effect on the velocity increment skewness in isotropic turbulence
Second and third order longitudinal structure functions and wavenumber
spectra of isotropic turbulence are computed using the EDQNM model and compared
to results of the multifractal formalism. At the highest Reynolds number
available in windtunnel experiments, , both the multifractal
model and EDQNM give power-law corrections to the inertial range scaling of the
velocity increment skewness. For EDQNM, this correction is a finite Reynolds
number effect, whereas for the multifractal formalism it is an intermittency
correction that persists at any high Reynolds number. Furthermore, the two
approaches yield realistic behavior of second and third order statistics of the
velocity fluctuations in the dissipative and near-dissipative ranges.
Similarities and differences are highlighted, in particular the Reynolds number
dependence
Binding branched and linear DNA structures: from isolated clusters to fully bonded gels
The proper design of DNA sequences allows for the formation of well defined
supramolecular units with controlled interactions via a consecution of
self-assembling processes. Here, we benefit from the controlled DNA
self-assembly to experimentally realize particles with well defined valence,
namely tetravalent nanostars (A) and bivalent chains (B). We specifically focus
on the case in which A particles can only bind to B particles, via
appropriately designed sticky-end sequences. Hence AA and BB bonds are not
allowed. Such a binary mixture system reproduces with DNA-based particles the
physics of poly-functional condensation, with an exquisite control over the
bonding process, tuned by the ratio, r, between B and A units and by the
temperature, T. We report dynamic light scattering experiments in a window of
Ts ranging from 10{\deg}C to 55{\deg}C and an interval of r around the
percolation transition to quantify the decay of the density correlation for the
different cases. At low T, when all possible bonds are formed, the system
behaves as a fully bonded network, as a percolating gel and as a cluster fluid
depending on the selected r.Comment: 15 pages, 11 figure
Random Time Forward Starting Options
We introduce a natural generalization of the forward-starting options, first
discussed by M. Rubinstein. The main feature of the contract presented here is
that the strike-determination time is not fixed ex-ante, but allowed to be
random, usually related to the occurrence of some event, either of financial
nature or not. We will call these options {\bf Random Time Forward Starting
(RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis,
we can exhibit arbitrage free prices, which can be explicitly computed in many
classical market models, at least under independence between the random time
and the assets' prices. Practical implementations of the pricing methodologies
are also provided. Finally a credit value adjustment formula for these OTC
options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur
Dynamic multilateral markets
We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
We propose a mathematical derivation of Brinkman's force for a cloud of
particles immersed in an incompressible fluid. Our starting point is the Stokes
or steady Navier-Stokes equations set in a bounded domain with the disjoint
union of N balls of radius 1/N removed, and with a no-slip boundary condition
for the fluid at the surface of each ball. The large N limit of the fluid
velocity field is governed by the same (Navier-)Stokes equations in the whole
domain, with an additional term (Brinkman's force) that is (minus) the total
drag force exerted by the fluid on the particle system. This can be seen as a
generalization of Allaire's result in [Arch. Rational Mech. Analysis 113
(1991), 209-259] who treated the case of motionless, periodically distributed
balls. Our proof is based on slightly simpler, though similar homogenization
techniques, except that we avoid the periodicity assumption and use instead the
phase-space empirical measure for the particle system. Similar equations are
used for describing the fluid phase in various models for sprays
Recommended from our members
Performance of Electronic Ballast and Controls with 34 and 40 watt F40 Fluorescent Lamps
Investigation of methods to produce a uniform cloud of fuel particles in a flame tube
The combustion of a uniform, quiescent cloud of 30-micron fuel particles in a flame tube was proposed as a space-based, low-gravity experiment. The subject is the normal- and low-gravity testing of several methods to produce such a cloud, including telescoping propeller fans, air pumps, axial and quadrature acoustical speakers, and combinations of these devices. When operated in steady state, none of the methods produced an acceptably uniform cloud (+ or - 5 percent of the mean concentration), and voids in the cloud were clearly visible. In some cases, severe particle agglomeration was observed; however, these clusters could be broken apart by a short acoustic burst from an axially in-line speaker. Analyses and experiments reported elsewhere suggest that transient, acoustic mixing methods can enhance cloud uniformity while minimizing particle agglomeration
- …