Application of a Parametric Level-Set Approach to Topology Optimization of Fluids with the Navier–Stokes and Lattice Boltzmann Equations

Traditional material distribution based methods applied to the topology optimization of fluidic systems often suffer from rather slow convergence. The local influence of the design variables in the traditional material distribution based approaches is seen as the primary cause, leading to small gradients which cannot drive the optimization process sufficiently. The present work is an attempt to improve the rate of convergence of topology optimization methods of fluidic systems by employing a parametric level-set function coupled with a topology description approach. Using level-set methods, a global impact of design variables is achieved and the material description is decoupled from the flow field discretization. This promises to improve the gradients with respect to the design variables and can be applied to rather different types of fluid formulations and discretization methods. In the present work, a finite element method for solving the Navier-Stokes equations and a hydrodynamic finite difference lattice Boltzmann method are considered. Using a 2D example the parametric level-set approach is validated through comparison with traditional material distribution based methods. While the parametric level-set approach leads to the desired optimal designs and has advantages such as improved modularity and smoothness of design boundaries when compared to material distribution based methods, the present study does not reveal improvements for the convergence of the optimization problem

The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground state energy in terms of the Jost function of the related scattering problem. Then we find the corresponding heat kernel coefficients and perform the renormalization, imposing the normalization condition that the ground state energy vanishes when the mass of the quantum field becomes large. Finally the ground state energy is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials.Comment: 15 pages, 5 figure

Practical isogeometric shape optimization: Parameterization by means of regularization

International audienceShape optimization based on Isogeometric Analysis (IGA) has gained popularity in recent years. Performing shape optimization directly over parameters defining the CAD geometry, such as for example the control points of a spline parametrization, opens up the prospect of seamless integration of a shape optimization step into the CAD workflow. One of the challenges when using IGA for shape optimization is that of maintaining a valid geometry parametrization of the interior of the domain during an optimization process, as the shape of the boundary is altered by an optimization algorithm. Existing methods impose constraints on the Jacobian of the parametrization, to guarantee that the parametrization remains valid. The number of such validity constraints quickly becomes intractably large, especially when 3D shape optimization problems are considered. An alternative, and arguably simpler, approach is to formulate the isogeometric shape optimization problem in terms of both the boundary and the interior control points. In order to ensure a geometric parametrization of sufficient quality a regularization term, such as the Winslow functional, is added to the objective function of the shape optimization problem. We illustrate the performance of these methods on the optimal design problem of electromagnetic reflectors and compare their performance. Both methods are implemented for multipatch geometries, using the IGA library G+Smo and the optimization library Ipopt. We find that the second approach performs comparably to a state of the art method with respect to both the quality of the found solutions and computational time, while its performance in our experience is more robust for coarse discretizations

Identification of genes important for growth of asymptomatic Bacteriuria Escherichia coli in urine

Escherichia coli is the most important etiological agent of urinary tract infections (UTIs). Unlike uropathogenic E. coli, which causes symptomatic infections, asymptomatic bacteriuria (ABU) E. coli strains typically lack essential virulence factors and colonize the bladder in the absence of symptoms. While ABU E. coli can persist in the bladder for long periods of time, little is known about the genetic determinants required for its growth and fitness in urine. To identify such genes, we have employed a transposon mutagenesis approach using the prototypic ABU E. coli strain 83972 and the clinical ABU E. coli strain VR89. Six genes involved in the biosynthesis of various amino acids and nucleobases were identified (carB, argE, argC, purA, metE, and ilvC), and site-specific mutants were subsequently constructed in E. coli 83972 and E. coli VR89 for each of these genes. In all cases, these mutants exhibited reduced growth rates and final cell densities in human urine. The growth defects could be complemented in trans as well as by supplementation with the appropriate amino acid or nucleobase. When assessed in vivo in a mouse model, E. coli 83972carAB and 83972argC showed a significantly reduced competitive advantage in the bladder and/or kidney during coinoculation experiments with the parent strain, whereas 83972metE and 83972ilvC did not. Taken together, our data have identified several biosynthesis pathways as new important fitness factors associated with the growth of ABU E. coli in human urine

Chiral tunneling in single and bilayer graphene

We review chiral (Klein) tunneling in single-layer and bilayer graphene and present its semiclassical theory, including the Berry phase and the Maslov index. Peculiarities of the chiral tunneling are naturally explained in terms of classical phase space. In a one-dimensional geometry we reduced the original Dirac equation, describing the dynamics of charge carriers in the single layer graphene, to an effective Schr\"odinger equation with a complex potential. This allowed us to study tunneling in details and obtain analytic formulas. Our predictions are compared with numerical results. We have also demonstrated that, for the case of asymmetric n-p-n junction in single layer graphene, there is total transmission for normal incidence only, side resonances are suppressed.Comment: submitted to Proceedings of Nobel Symposium on graphene, May 201

Single-neuron RNA-Seq: technical feasibility and reproducibility

Understanding brain function involves improved knowledge about how the genome specifies such a large diversity of neuronal types. Transcriptome analysis of single neurons has been previously described using gene expression microarrays. Using high-throughput transcriptome sequencing (RNA-Seq), we have developed a method to perform single-neuron RNA-Seq. Following electrophysiology recording from an individual neuron, total RNA was extracted by aspirating the cellular contents into a fine glass electrode tip. The mRNAs were reverse transcribed and amplified to construct a single neuron cDNA library, and subsequently subjected to high-throughput sequencing. This approach was applicable to both individual neurons cultured from embryonic mouse hippocampus, as well as neocortical neurons from live brain slices. We found that the average pairwise Spearman’s rank correlation coefficient of gene expression level expressed as RPKM (reads per kilobase of transcript per million mapped reads) was 0.51 between five cultured neuronal cells, whereas the same measure between three cortical layer V neurons in situ was 0.25. The data suggest that there may be greater heterogeneity of the cortical neurons, as compared to neurons in vitro. The results demonstrate the technical feasibility and reproducibility of RNA-Seq in capturing a part of the transcriptome landscape of single neurons, and confirmed that morphologically identical neurons, even from the same region, have distinct gene expression patterns

Casimir effect in deformed field

The Casimir energy is calculated in one-, two-, and three-dimensional spaces for the field with generalized coordinates and momenta satisfying the deformed Poisson brackets leading to the minimal length.Comment: 12 pages, 1 figur

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio