72,231 research outputs found
Rain water transport and storage in a model sandy soil with hydrogel particle additives
We study rain water infiltration and drainage in a dry model sandy soil with
superabsorbent hydrogel particle additives by measuring the mass of retained
water for non-ponding rainfall using a self-built 3D laboratory set-up. In the
pure model sandy soil, the retained water curve measurements indicate that
instead of a stable horizontal wetting front that grows downward uniformly, a
narrow fingered flow forms under the top layer of water-saturated soil. This
rain water channelization phenomenon not only further reduces the available
rain water in the plant root zone, but also affects the efficiency of soil
additives, such as superabsorbent hydrogel particles. Our studies show that the
shape of the retained water curve for a soil packing with hydrogel particle
additives strongly depends on the location and the concentration of the
hydrogel particles in the model sandy soil. By carefully choosing the particle
size and distribution methods, we may use the swollen hydrogel particles to
modify the soil pore structure, to clog or extend the water channels in sandy
soils, or to build water reservoirs in the plant root zone
Effect of hydrogel particle additives on water-accessible pore structure of sandy soils: A custom pressure plate apparatus and capillary bundle model
To probe the effects of hydrogel particle additives on the water-accessible
pore structure of sandy soils, we introduce a custom pressure plate method in
which the volume of water expelled from a wet granular packing is measured as a
function of applied pressure. Using a capillary bundle model, we show that the
differential change in retained water per pressure increment is directly
related to the cumulative cross-sectional area distribution of the
water-accessible pores with radii less than . This is validated by
measurements of water expelled from a model sandy soil composed of 2 mm
diameter glass beads. In particular, the expelled water is found to depend
dramatically on sample height and that analysis using the capillary bundle
model gives the same pore size distribution for all samples. The distribution
is found to be approximately log-normal, and the total cross-sectional area
fraction of the accessible pore space is found to be . We then report
on how the pore distribution and total water-accessible area fraction are
affected by superabsorbent hydrogel particle additives, uniformly mixed into a
fixed-height sample at varying concentrations. Under both fixed volume and free
swelling conditions, the total area fraction of water-accessible pore space in
a packing decreases exponentially as the gel concentration increases. The size
distribution of the pores is significantly modified by the swollen hydrogel
particles, such that large pores are clogged while small pores are formed
The Ultraviolet flash accompanying GRBs from neutron-rich internal shocks
In the neutron-rich internal shocks model for Gamma-ray Burts (GRBs), the
Lorentz factors (LFs) of ions shells are variable, so are the LFs of
accompanying neutron shells. For slow neutron shells with a typical LF tens,
the typical beta-decay radius reads R_{\beta,s} several 10^{14} cm, which is
much larger than the typical internal shocks radius 10^{13} cm, so their impact
on the internal shocks may be unimportant. However, as GRBs last long enough
(T_{90}>20(1+z) s), one earlier but slower ejected neutron shell will be swept
successively by later ejected ion shells in the range 10^{13}-10^{15} cm, where
slow neutrons have decayed significantly. We show in this work that ion shells
interacting with the beta-decay products of slow neutron shells can power a
ultraviolet (UV) flash bright to 12th magnitude during the prompt gamma-ray
emission phase or slightly delayed, which can be detected by the upcoming
Satellite SWIFT in the near future.Comment: 6 pages (2 eps figures), accepted for publication in ApJ
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Stability Analysis of Turing Patterns Generated by the Schnakenberg Model
We consider the following Schnakenberg model on the interval (−1, 1): ut = D1u − u + vu2 in (−1, 1), vt = D2v + B − vu2 in (−1, 1), u (−1) = u (1) = v (−1) = v (1) = 0, where D1 > 0, D2 > 0, B>0. We rigorously show that the stability of symmetric N−peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1,D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations
Towards Identification of Relevant Variables in the observed Aerosol Optical Depth Bias between MODIS and AERONET observations
Measurements made by satellite remote sensing, Moderate Resolution Imaging
Spectroradiometer (MODIS), and globally distributed Aerosol Robotic Network
(AERONET) are compared. Comparison of the two datasets measurements for aerosol
optical depth values show that there are biases between the two data products.
In this paper, we present a general framework towards identifying relevant set
of variables responsible for the observed bias. We present a general framework
to identify the possible factors influencing the bias, which might be
associated with the measurement conditions such as the solar and sensor zenith
angles, the solar and sensor azimuth, scattering angles, and surface
reflectivity at the various measured wavelengths, etc. Specifically, we
performed analysis for remote sensing Aqua-Land data set, and used machine
learning technique, neural network in this case, to perform multivariate
regression between the ground-truth and the training data sets. Finally, we
used mutual information between the observed and the predicted values as the
measure of similarity to identify the most relevant set of variables. The
search is brute force method as we have to consider all possible combinations.
The computations involves a huge number crunching exercise, and we implemented
it by writing a job-parallel program
Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation
The classical dynamics for a charged point particle with intrinsic spin is
governed by a relativistic Hamiltonian for the orbital motion and by the
Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is
natural to ask whether the classical Hamiltonian (with both the orbital and
spin parts) is consistent with that in the relativistic quantum theory for a
spin-1/2 charged particle, which is described by the Dirac equation. In the
low-energy limit, up to terms of the 7th order in ( and
is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation
of the Dirac Hamiltonian in the presence of homogeneous and static
electromagnetic fields and show that it is indeed in agreement with the
classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through
electromagnetic duality, this result can be generalized for a spin-1/2 dyon,
which has both electric and magnetic charges and thus possesses both intrinsic
electric and magnetic dipole moments. Furthermore, the relativistic quantum
theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and
gyroelectric ratios can be described by the Dirac-Pauli equation, which is the
Dirac equation with augmentation for the anomalous electric and anomalous
magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian
is shown, up to the 7th order again, to be also in accord with the classical
Hamiltonian.Comment: 18 page
Existence and Stability of a Spike in the Central Component for a Consumer Chain Model
We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir
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