124,894 research outputs found
From Elasticity to Hypoplasticity: Dynamics of Granular Solids
"Granular elasticity," useful for calculating static stress distributions in
granular media, is generalized by including the effects of slowly moving,
deformed grains. The result is a hydrodynamic theory for granular solids that
agrees well with models from soil mechanics
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
Dynamic Linkages in Credit Risk: Modeling the Time-Varying Correlation between the Money and Derivatives Markets over the Crisis Period
This paper examines the dynamic linkages in credit risk between the money market and the derivatives market during 2004–9. We use the T-bill–Eurodollar (TED) spread to measure credit risk in the money market and the credit default swap (CDS) index spread for the derivatives market. The linkages are measured by a dynamic conditional correlation–Glosten–Jagannathan–Runkle–generalized auto regressive conditional heteroscedasticity model. The results show that the correlation between the TED spread and the CDS index spread fluctuated around zero prior to the crisis. While the correlation increased before the crisis, it moved notably higher during the crisis. Finally, the correlation fell in early 2009 but persisted at a level between 0.05 and 0.1, higher than the precrisis period
Monte-Carlo approach to calculate the proton stopping in warm dense matter within particle-in-cell simulations
A Monte-Carlo approach to proton stopping in warm dense matter is implemented
into an existing particle-in-cell code. The model is based on multiple
binary-collisions among electron-electron, electron-ion and ion-ion, taking
into account contributions from both free and bound electrons, and allows to
calculate particle stopping in much more natural manner. At low temperature
limit, when ``all'' electron are bounded at the nucleus, the stopping power
converges to the predictions of Bethe-Bloch theory, which shows good
consistency with data provided by the NIST. With the rising of temperatures,
more and more bound electron are ionized, thus giving rise to an increased
stopping power to cold matter, which is consistent with the report of a
recently experimental measurement [Phys. Rev. Lett. 114, 215002 (2015)]. When
temperature is further increased, with ionizations reaching the maximum,
lowered stopping power is observed, which is due to the suppression of
collision frequency between projected proton beam and hot plasmas in the
target.Comment: 6 pages, 4 figure
Monte-Carlo approach to calculate the ionization of warm dense matter within particle-in-cell simulations
A physical model based on a Monte-Carlo approach is proposed to calculate the
ionization dynam- ics of warm dense matters (WDM) within particle-in-cell
simulations, and where the impact (col- lision) ionization (CI), electron-ion
recombination (RE) and ionization potential depression (IPD) by surrounding
plasmas are taken into consideration self-consistently. When compared with
other models, which are applied in the literature for plasmas near thermal
equilibrium, the temporal re- laxation of ionization dynamics can also be
simulated by the proposed model. Besides, this model is general and can be
applied for both single elements and alloys with quite different composi-
tions. The proposed model is implemented into a particle-in-cell (PIC) code,
with (final) ionization equilibriums sustained by competitions between CI and
its inverse process (i.e., RE). Comparisons between the full model and model
without IPD or RE are performed. Our results indicate that for bulk aluminium
in the WDM regime, i) the averaged ionization degree increases by including
IPD; while ii) the averaged ionization degree is significantly over estimated
when the RE is neglected. A direct comparison from the PIC code is made with
the existing models for the dependence of averaged ionization degree on thermal
equilibrium temperatures, and shows good agreements with that generated from
Saha-Boltzmann model or/and FLYCHK code.Comment: 7 pages, 4 figure
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