855 research outputs found
Relation Between Bulk and Interface Descriptions of Alloy Solidification
From a simple bulk model for the one-dimensional steady-state solidification
of a dilute binary alloy we derive an interface description, allowing arbitrary
values of the growth velocity. Our derivation leads to exact expressions for
the fluxes and forces at the interface and for the set of Onsager coefficients.
We, moreover, discover a continuous symmetry, which appears in the low-velocity
regime, and there deletes the Onsager sign and symmetry properties. An example
is the generation of the sometimes negative friction coefficient in the
crystallization flux-force relation
Diffusion-Induced Oscillations of Extended Defects
From a simple model for the driven motion of a planar interface under the
influence of a diffusion field we derive a damped nonlinear oscillator equation
for the interface position. Inside an unstable regime, where the damping term
is negative, we find limit-cycle solutions, describing an oscillatory
propagation of the interface. In case of a growing solidification front this
offers a transparent scenario for the formation of solute bands in binary
alloys, and, taking into account the Mullins-Sekerka instability, of banded
structures
Postcard: Don Smith Republican for Attorney General
This black and white photographic postcard portrays an orange background. The right side features a black and white picture of Don Smith\u27s wife and three children in a group portrait. A woman sits on a chair and a girl stands to her right. A girl sits on a stool in front of the woman. A boy stands behind and to the left of the woman. Books on bookshelves are in the background. The right side of the picture depicts a black and white photo of a man\u27s head. A cartoon illustration of an elephant\u27s head is in the middle of the card. Printed text is on the left side of the card. Printed text and handwriting is on the back of the card.https://scholars.fhsu.edu/tj_postcards/1633/thumbnail.jp
Hamiltonian simulation algorithms for near-term quantum hardware
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below” the circuit model, exploiting the underlying control over qubit interactions available in most quantum hardware and deriving analytic circuit identities for synthesising multi-qubit evolutions from two-qubit interactions. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to time-dynamics simulation of the 2D spin Fermi-Hubbard model. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and an analysis of error propagation, we find that e.g. for a 5 × 5 Fermi-Hubbard lattice we reduce the circuit depth from 1, 243, 586 using the best previous fermion encoding and error bounds in the literature, to 3, 209 in the per-gate error model, or the circuit-depth-equivalent to 259 in the per-time error model. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era
Capillary-Wave Model for the Solidification of Dilute Binary Alloys
Starting from a phase-field description of the isothermal solidification of a
dilute binary alloy, we establish a model where capillary waves of the
solidification front interact with the diffusive concentration field of the
solute. The model does not rely on the sharp-interface assumption, and includes
non-equilibrium effects, relevant in the rapid-growth regime. In many
applications it can be evaluated analytically, culminating in the appearance of
an instability which, interfering with the Mullins-Sekerka instability, is
similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure
Capillary-Wave Description of Rapid Directional Solidification
A recently introduced capillary-wave description of binary-alloy
solidification is generalized to include the procedure of directional
solidification. For a class of model systems a universal dispersion relation of
the unstable eigenmodes of a planar steady-state solidification front is
derived, which readjusts previously known stability considerations. We,
moreover, establish a differential equation for oscillatory motions of a planar
interface that offers a limit-cycle scenario for the formation of solute bands,
and, taking into account the Mullins-Sekerka instability, of banded structures
Microrheology, stress fluctuations and active behavior of living cells
We report the first measurements of the intrinsic strain fluctuations of
living cells using a recently-developed tracer correlation technique along with
a theoretical framework for interpreting such data in heterogeneous media with
non-thermal driving. The fluctuations' spatial and temporal correlations
indicate that the cytoskeleton can be treated as a course-grained continuum
with power-law rheology, driven by a spatially random stress tensor field.
Combined with recent cell rheology results, our data imply that intracellular
stress fluctuations have a nearly power spectrum, as expected for
a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let
On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua
Linear combinations of chi square random variables occur in a wide range of
fields. Unfortunately, a closed, analytic expression for the pdf is not yet
known. As a first result of this work, an explicit analytic expression for the
density of the sum of two gamma random variables is derived. Then a
computationally efficient algorithm to numerically calculate the linear
combination of chi square random variables is developed. An explicit expression
for the error bound is obtained. The proposed technique is shown to be
computationally efficient, i.e. only polynomial in growth in the number of
terms compared to the exponential growth of most other methods. It provides a
vast improvement in accuracy and shows only logarithmic growth in the required
precision. In addition, it is applicable to a much greater number of terms and
currently the only way of computing the distribution for hundreds of terms. As
an application, the exponential dependence of the eigenvalue fluctuation
probability of a random matrix model for 4d supergravity with N scalar fields
is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio
Evapotranspiration of native vegetation in the closed basin of the San Luis Valley, Colorado
June 1987.Bibliography: page 21.Grant nos. 14-08-001-G895 and 14-08-0001-G1006; project no. 06; financed in part by the U.S. Department of the Interior, Geological Survey and Bureau of Reclamation, through the Colorado Water Resources Research Institute in cooperation with the U.S.D.A. Agricultural Research Service
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