4,026 research outputs found
Challenges in imaging and predictive modeling of rhizosphere processes
Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes
Inherent-Structure Dynamics and Diffusion in Liquids
The self-diffusion constant D is expressed in terms of transitions among the
local minima of the potential (inherent structure, IS) and their correlations.
The formulae are evaluated and tested against simulation in the supercooled,
unit-density Lennard-Jones liquid. The approximation of uncorrelated
IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature
range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST
are associated with a hopping mechanism, the condition D ~ D_{0} provides a new
way to identify the crossover to hopping. The results suggest that theories of
diffusion in deeply supercooled liquids may be based on weakly correlated IST.Comment: submitted to PR
Electron-Acoustic Phonon Energy Loss Rate in Multi-Component Electron Systems with Symmetric and Asymmetric Coupling Constants
We consider electron-phonon (\textit{e-ph}) energy loss rate in 3D and 2D
multi-component electron systems in semiconductors. We allow general asymmetry
in the \textit{e-ph} coupling constants (matrix elements), i.e., we allow that
the coupling depends on the electron sub-system index. We derive a
multi-component \textit{e-ph}power loss formula, which takes into account the
asymmetric coupling and links the total \textit{e-ph} energy loss rate to the
density response matrix of the total electron system. We write the density
response matrix within mean field approximation, which leads to coexistence of\
symmetric energy loss rate and asymmetric energy loss rate
with total energy loss rate at temperature
. The symmetric component F_{S}(T) F_{S}(T)\propto T^{n_{S}}n_{S}F_{A}(T). Screening strongly
reduces the symmetric coupling, but the asymmetric coupling is unscreened,
provided that the inter-sub-system Coulomb interactions are strong. The lack of
screening enhances and the total energy loss rate .
Especially, in the strong screening limit we find . A
canonical example of strongly asymmetric \textit{e-ph} matrix elements is the
deformation potential coupling in many-valley semiconductors.Comment: v2: Typos corrected. Some notations changed. Section III.C is
embedded in Section III.B. Paper accepted to PR
Potential energy landscape-based extended van der Waals equation
The inherent structures ({\it IS}) are the local minima of the potential
energy surface or landscape, , of an {\it N} atom system.
Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the
implications for the equation of state are investigated. It is shown that the
van der Waals ({\it vdW}) equation, with density-dependent and
coefficients, holds on the high-temperature plateau of the averaged {\it IS}
energy. However, an additional ``landscape'' contribution to the pressure is
found at lower . The resulting extended {\it vdW} equation, unlike the
original, is capable of yielding a water-like density anomaly, flat isotherms
in the coexistence region {\it vs} {\it vdW} loops, and several other desirable
features. The plateau energy, the width of the distribution of {\it IS}, and
the ``top of the landscape'' temperature are simulated over a broad reduced
density range, , in the Lennard-Jones fluid. Fits to the
data yield an explicit equation of state, which is argued to be useful at high
density; it nevertheless reproduces the known values of and at the
critical point
The Potential Energy Landscape and Mechanisms of Diffusion in Liquids
The mechanism of diffusion in supercooled liquids is investigated from the
potential energy landscape point of view, with emphasis on the crossover from
high- to low-T dynamics. Molecular dynamics simulations with a time dependent
mapping to the associated local mininum or inherent structure (IS) are
performed on unit-density Lennard-Jones (LJ). New dynamical quantities
introduced include r2_{is}(t), the mean-square displacement (MSD) within a
basin of attraction of an IS, R2(t), the MSD of the IS itself, and g_{loc}(t)
the mean waiting time in a cooperative region. At intermediate T, r2_{is}(t)
posesses an interval of linear t-dependence allowing calculation of an
intrabasin diffusion constant D_{is}. Near T_{c} diffusion is intrabasin
dominated with D = D_{is}. Below T_{c} the local waiting time tau_{loc} exceeds
the time, tau_{pl}, needed for the system to explore the basin, indicating the
action of barriers. The distinction between motion among the IS below T_{c} and
saddle, or border dynamics above T_{c} is discussed.Comment: submitted to pr
Single spin universal Boolean logic
Recent advances in manipulating single electron spins in quantum dots have
brought us close to the realization of classical logic gates based on
representing binary bits in spin polarizations of single electrons. Here, we
show that a linear array of three quantum dots, each containing a single spin
polarized electron, and with nearest neighbor exchange coupling, acts as the
universal NAND gate. The energy dissipated during switching this gate is the
Landauer-Shannon limit of kTln(1/p) [T = ambient temperature and p = intrinsic
gate error probability]. With present day technology, p = 1E-9 is achievable
above 1 K temperature. Even with this small intrinsic error probability, the
energy dissipated during switching the NAND gate is only ~ 21 kT, while today's
nanoscale transistors dissipate about 40,000 - 50,000 kT when they switch
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
opens new avenues for introducing INM into dynamical theories. Liquid 'states'
are usually defined by assigning a configuration to the minimum to which it
will drain, but the REM naturally treats saddle-barriers on the same footing as
minima, which may be a better mapping of the continuum of configurations to
discrete states. Requirements of a detailed REM description of liquids are
discussed
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Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner
Instantaneous Normal Mode analysis of liquid HF
We present an Instantaneous Normal Modes analysis of liquid HF aimed to
clarify the origin of peculiar dynamical properties which are supposed to stem
from the arrangement of molecules in linear hydrogen-bonded network. The
present study shows that this approach is an unique tool for the understanding
of the spectral features revealed in the analysis of both single molecule and
collective quantities. For the system under investigation we demonstrate the
relevance of hydrogen-bonding ``stretching'' and fast librational motion in the
interpretation of these features.Comment: REVTeX, 7 pages, 5 eps figures included. Minor changes in the text
and in a figure. Accepted for publication in Phys. Rev. Let
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