7,053 research outputs found
Lattice Boltzmann Simulations of Droplet formation in confined Channels with Thermocapillary flows
Based on mesoscale lattice Boltzmann simulations with the "Shan-Chen" model,
we explore the influence of thermocapillarity on the break-up properties of
fluid threads in a microfluidic T-junction, where a dispersed phase is injected
perpendicularly into a main channel containing a continuous phase, and the
latter induces periodic break-up of droplets due to the cross-flowing.
Temperature effects are investigated by switching on/off both positive/negative
temperature gradients along the main channel direction, thus promoting a
different thread dynamics with anticipated/delayed break-up. Numerical
simulations are performed at changing the flow-rates of both the continuous and
dispersed phases, as well as the relative importance of viscous forces, surface
tension forces and thermocapillary stresses. The range of parameters is broad
enough to characterize the effects of thermocapillarity on different mechanisms
of break-up in the confined T-junction, including the so-called "squeezing" and
"dripping" regimes, previously identified in the literature. Some simple
scaling arguments are proposed to rationalize the observed behaviour, and to
provide quantitative guidelines on how to predict the droplet size after
break-up.Comment: 18 pages, 9 figure
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
Replacing linear diffusion by a degenerate diffusion of porous medium type is
known to regularize the classical two-dimensional parabolic-elliptic
Keller-Segel model. The implications of nonlinear diffusion are that solutions
exist globally and are uniformly bounded in time. We analyse the stationary
case showing the existence of a unique, up to translation, global minimizer of
the associated free energy. Furthermore, we prove that this global minimizer is
a radially decreasing compactly supported continuous density function which is
smooth inside its support, and it is characterized as the unique compactly
supported stationary state of the evolution model. This unique profile is the
clear candidate to describe the long time asymptotics of the diffusion
dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure
Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol
We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in
two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change
in the viscosity with temperature. The results are presented both as functions
of the Rayleigh number (Ra) up to (for fixed temperature difference
between the top and bottom plates) and as functions of
"non-Oberbeck-Boussinesqness'' or "NOBness'' () up to 50 K (for fixed
Ra). For this large NOBness the center temperature is more than 5 K
larger than the arithmetic mean temperature between top and bottom plate
and only weakly depends on Ra. To physically account for the NOB deviations of
the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the
decomposition of into the product of two effects, namely
first the change in the sum of the top and bottom thermal BL thicknesses, and
second the shift of the center temperature as compared to . While
for water the origin of the deviation is totally dominated by the second
effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the
first effect is dominating, in spite of the large increase of as compared
to .Comment: 6 pages, 7 figure
A Proposal for an ADU Incentive Program for the City of Mill Valley
The development of Accessory Dwelling Units (ADUs) is an important option for responding to increases in housing demand, increasing the diversity in housing options, broadening the range of space available, addressing varied financial needs, and increasing density
{\delta}N formalism
Precise understanding of nonlinear evolution of cosmological perturbations
during inflation is necessary for the correct interpretation of measurements of
non-Gaussian correlations in the cosmic microwave background and the
large-scale structure of the universe. The "{\delta}N formalism" is a popular
and powerful technique for computing non-linear evolution of cosmological
perturbations on large scales. In particular, it enables us to compute the
curvature perturbation, {\zeta}, on large scales without actually solving
perturbed field equations. However, people often wonder why this is the case.
In order for this approach to be valid, the perturbed Hamiltonian constraint
and matter-field equations on large scales must, with a suitable choice of
coordinates, take on the same forms as the corresponding unperturbed equations.
We find that this is possible when (1) the unperturbed metric is given by a
homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker metric; and (2)
on large scales and with a suitable choice of coordinates, one can ignore the
shift vector (g0i) as well as time-dependence of tensor perturbations to
gij/a2(t) of the perturbed metric. While the first condition has to be assumed
a priori, the second condition can be met when (3) the anisotropic stress
becomes negligible on large scales. However, in order to explicitly show that
the second condition follows from the third condition, one has to use
gravitational field equations, and thus this statement may depend on the
details of theory of gravitation. Finally, as the {\delta}N formalism uses only
the Hamiltonian constraint and matter-field equations, it does not a priori
respect the momentum constraint. We show that the violation of the momentum
constraint only yields a decaying mode solution for {\zeta}, and the violation
vanishes when the slow-roll conditions are satisfied.Comment: 10 page
Generating sequential space-filling designs using genetic algorithms and Monte Carlo methods
In this paper, the authors compare a Monte Carlo method and an optimization-based approach using genetic algorithms for sequentially generating space-filling experimental designs. It is shown that Monte Carlo methods perform better than genetic algorithms for this specific problem
On Minimizing Crossings in Storyline Visualizations
In a storyline visualization, we visualize a collection of interacting
characters (e.g., in a movie, play, etc.) by -monotone curves that converge
for each interaction, and diverge otherwise. Given a storyline with
characters, we show tight lower and upper bounds on the number of crossings
required in any storyline visualization for a restricted case. In particular,
we show that if (1) each meeting consists of exactly two characters and (2) the
meetings can be modeled as a tree, then we can always find a storyline
visualization with crossings. Furthermore, we show that there
exist storylines in this restricted case that require
crossings. Lastly, we show that, in the general case, minimizing the number of
crossings in a storyline visualization is fixed-parameter tractable, when
parameterized on the number of characters . Our algorithm runs in time
, where is the number of meetings.Comment: 6 pages, 4 figures. To appear at the 23rd International Symposium on
Graph Drawing and Network Visualization (GD 2015
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Nonlinear Evolution of Very Small Scale Cosmological Baryon Perturbations at Recombination
The evolution of baryon density perturbations on very small scales is
investigated. In particular, the nonlinear growth induced by the radiation drag
force from the shear velocity field on larger scales during the recombination
epoch, which is originally proposed by Shaviv in 1998, is studied in detail. It
is found that inclusion of the diffusion term which Shaviv neglected in his
analysis results in rather mild growth whose growth rate is instead
of enormous amplification of Shaviv's original claim since the
diffusion suppresses the growth. The growth factor strongly depends on the
amplitude of the large scale velocity field. The nonlinear growth mechanism is
applied to density perturbations of general adiabatic cold dark matter (CDM)
models. In these models, it has been found in the previous works that the
baryon density perturbations are not completely erased by diffusion damping if
there exists gravitational potential of CDM. With employing the perturbed rate
equation which is derived in this paper, the nonlinear evolution of baryon
density perturbations is investigated. It is found that: (1) The nonlinear
growth is larger for smaller scales. This mechanism only affects the
perturbations whose scales are smaller than , which are
coincident with the stellar scales. (2) The maximum growth factors of baryon
density fluctuations for various COBE normalized CDM models are typically less
than factor 10 for large scale velocity peaks. (3) The growth factor
depends on .Comment: 24 pages, 9 figures, submitted to Ap
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