Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.

Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Nuttier Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright (C) 2010 John Wiley & Sons, Ltd.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

A Triangulation of CP3 as Symmetric Cube of S-2

The symmetric group acts on the Cartesian product (S (2)) (d) by coordinate permutation, and the quotient space is homeomorphic to the complex projective space a'',P (d) . We used the case d=2 of this fact to construct a 10-vertex triangulation of a'',P (2) earlier. In this paper, we have constructed a 124-vertex simplicial subdivision of the 64-vertex standard cellulation of (S (2))(3), such that the -action on this cellulation naturally extends to an action on . Further, the -action on is ``good'', so that the quotient simplicial complex is a 30-vertex triangulation of a'',P (3). In other words, we have constructed a simplicial realization of the branched covering (S (2))(3)-> a'',P (3).

Spatial memory deficits in maternal iron deficiency paradigms are associated with altered glucocorticoid levels

``The goal of this study was to examine the effect of maternal iron deficiency on the developing hippocampus in order to define a developmental window for this effect, and to see whether iron deficiency causes changes in glucocorticoid levels. The study was carried out using pre-natal, post-natal, and pre + post-natal iron deficiency paradigm. Iron deficient pregnant dams and their pups displayed elevated corticosterone which, in turn, differentially affected glucocorticoid receptor (GR) expression in the CA1 and the dentate gyrus. Brain Derived Neurotrophic Factor (BDNF) was reduced in the hippocampi of pups following elevated corticosterone levels. Reduced neurogenesis at P7 was seen in pups born to iron deficient mothers, and these pups had reduced numbers of hippocampal pyramidal and granule cells as adults. Hippocampal subdivision volumes also were altered. The structural and molecular defects in the pups were correlated with radial arm maze performance; reference memory function was especially affected. Pups from dams that were iron deficient throughout pregnancy and lactation displayed the complete spectrum of defects, while pups from dams that were iron deficient only during pregnancy or during lactation displayed subsets of defects. These findings show that maternal iron deficiency is associated with altered levels of corticosterone and GR expression, and with spatial memory deficits in their pups.'' (C) 2013 Elsevier Inc. All rights reserved.

Efficient simulation and rendering of realistic motion of one-dimensional flexible objects

In gross motion of flexible one-dimensional (1D) objects such as cables, ropes, chains, ribbons and hair, the assumption of constant length is realistic and reasonable. The motion of the object also appears more natural if the motion or disturbance given at one end attenuates along the length of the object. In an earlier work, variational calculus was used to derive natural and length-preserving transformation of planar and spatial curves and implemented for flexible 1D objects discretized with a large number of straight segments. This paper proposes a novel idea to reduce computational effort and enable real-time and realistic simulation of the motion of flexible 1D objects. The key idea is to represent the flexible 1D object as a spline and move the underlying control polygon with much smaller number of segments. To preserve the length of the curve to within a prescribed tolerance as the control polygon is moved, the control polygon is adaptively modified by subdivision and merging. New theoretical results relating the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines. Depending on the prescribed tolerance on length error, the theoretical results are used to obtain threshold angles for subdivision and merging. Simulation results for arbitrarily chosen planar and spatial curves whose one end is subjected to generic input motions are provided to illustrate the approach. (C) 2016 Elsevier Ltd. All rights reserved.