Multi-objective engineering shape optimization using differential evolution interfaced to the Nimrod/O tool

This paper presents an enhancement of the Nimrod/O optimization tool by interfacing DEMO, an external multiobjective optimization algorithm. DEMO is a variant of differential evolution – an algorithm that has attained much popularity in the research community, and this work represents the first time that true multiobjective optimizations have been performed with Nimrod/O. A modification to the DEMO code enables multiple objectives to be evaluated concurrently. With Nimrod/O’s support for parallelism, this can reduce the wall-clock time significantly for compute intensive objective function evaluations. We describe the usage and implementation of the interface and present two optimizations. The first is a two objective mathematical function in which the Pareto front is successfully found after only 30 generations. The second test case is the three-objective shape optimization of a rib-reinforced wall bracket using the Finite Element software, Code_Aster. The interfacing of the already successful packages of Nimrod/O and DEMO yields a solution that we believe can benefit a wide community, both industrial and academic

A simplex-like search method for bi-objective optimization

We describe a new algorithm for bi-objective optimization, similar to the Nelder Mead simplex algorithm, widely used for single objective optimization. For diferentiable bi-objective functions on a continuous search space, internal Pareto optima occur where the two gradient vectors point in opposite directions. So such optima may be located by minimizing the cosine of the angle between these vectors. This requires a complex rather than a simplex, so we term the technique the \cosine seeking complex". An extra beneft of this approach is that a successful search identifes the direction of the effcient curve of Pareto points, expediting further searches. Results are presented for some standard test functions. The method presented is quite complicated and space considerations here preclude complete details. We hope to publish a fuller description in another place

Diffusion and Home Range Parameters from Rodent Population Measurements in Panama

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, \emph{Zygodontomys brevicauda}. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.Comment: 18 pages, 5 figure

Constructing Mutually Unbiased Bases in Dimension Six

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical approximations and corrected the number of triples existing for non-affine families (cf Table 3

Suture-method versus Through-the-needle Catheters for Continuous Popliteal-sciatic Nerve Blocks: A Randomized Clinical Trial.

BACKGROUND:The basic perineural catheter design has changed minimally since inception, with the catheter introduced through or over a straight needle. The U.S. Food and Drug Administration recently cleared a novel perineural catheter design comprising a catheter attached to the back of a suture-shaped needle that is inserted, advanced along the arc of its curvature pulling the catheter past the target nerve, and then exited through the skin in a second location. The authors hypothesized that analgesia would be noninferior using the new versus traditional catheter design in the first two days after painful foot/ankle surgery with a primary outcome of average pain measured with the Numeric Rating Scale. METHODS:Subjects undergoing painful foot or ankle surgery with a continuous supraparaneural popliteal-sciatic nerve block 5 cm proximal to the bifurcation were randomized to either a suture-type or through-the-needle catheter and subsequent 3-day 0.2% ropivacaine infusion (basal 6 ml/h, bolus 4 ml, lockout 30 min). Subjects received daily follow-up for the first four days after surgery, including assessment for evidence of malfunction or dislodgement of the catheters. RESULTS:During the first two postoperative days the mean ± SD average pain scores were lower in subjects with the suture-catheter (n = 35) compared with the through-the-needle (n = 35) group (2.7 ± 2.4 vs. 3.4 ± 2.4) and found to be statistically noninferior (95% CI, -1.9 to 0.6; P < 0.001). No suture-style catheter was completely dislodged (0%), whereas the tips of three (9%) traditional catheters were found outside of the skin before purposeful removal on postoperative day 3 (P = 0.239). CONCLUSIONS:Suture-type perineural catheters provided noninferior analgesia compared with traditional catheters for continuous popliteal-sciatic blocks after painful foot and ankle surgery. The new catheter design appears to be a viable alternative to traditional designs used for the past seven decades

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page