Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow

We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the non-permeability of the medium outside the fluid region. The resulting diffuse interface problem can be shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers and the optimality conditions. Additionally, we can derive a necessary optimality system for the sharp interface problem by geometric variations without stating additional regularity assumptions on the minimizing set

Numerical approximation of phase field based shape and topology optimization for fluids

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We formulate a corresponding optimization problem where flow outside the fluid domain is penalized. The resulting formulation of the shape optimization problem is shown to be well-posed, hence there exists a minimizer, and first order optimality conditions are derived. For the numerical realization we introduce a mass conserving gradient flow and obtain a Cahn--Hilliard type system, which is integrated numerically using the finite element method. An adaptive concept using reliable, residual based error estimation is exploited for the resolution of the spatial mesh. The overall concept is numerically investigated and comparison values are provided

Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field method uses a Ginzburg--Landau functional in order to approximate a perimeter penalization. We focus on surface functionals and carefully introduce a new modelling variant, show existence of minimizers and derive first order necessary conditions. These conditions are related to classical shape derivatives by identifying the sharp interface limit with the help of formally matched asymptotic expansions. Finally, we present numerical computations based on a Cahn--Hilliard type gradient descent which demonstrate that the method can be used to solve shape optimization problems for fluids with the help of the new approach

Optimal control of Allen-Cahn systems

Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented

Sharp interface limit for a phase field model in structural optimization

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of $\Gamma$-convergence of the reduced objective functional. Additionally, convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems

Billions (Yes, with a B) for Prevention, Victim Services, Law Enforcement, Underserved Populations and the Courts, and Looking ahead to VAWA IV

[panelist] I feel like I have gone on a trip down memory lane. I want to take us back in time to give you an idea of what it looked like for immigrant women, women of color, and underserved communities in 1994, in terms of access to services and assistance for domestic violence and sexual assault. In those days there were very few programs-and we could probably count them on two, maybe four hands nationally-that were working specifically and had expertise working with immigrant victims, non-English-speaking victims, and women of color victims. Those programs were isolated from each other. In 1994 I was working as a family lawyer at a program I helped found-AYUDA, a legal services agency serving the immigrant community in Washington, D.C. Janet Calvo was working with battered immigrants at CUNY Law School in New York, and in San Francisco the group of attorneys working will immigrant victims included Bill Tamayo at the Asian Law Caucus and Deeana Jang at the San Francisco Neighborhood Legal Assistance Foundation. Leni Matin and Debbie Lee at the Family Violence Prevention Fund teamed up with Martha Davis at Legal Momentum to bring us all together for a meeting to plan the first national conference on immigrant and refugee women\u27s rights that was held in Berkeley, California in 1991. This conference was the first effort nationally to bring together those of us working with immigrant populations and refugee populations

Automated Image Analysis of Transmission Electron Micrographs: Nanoscale Evaluation of Radiation-Induced DNA Damage in the Context of Chromatin

Background: Heavy ion irradiation (IR) with high-linear energy transfer (LET) is characterized by a unique depth dose distribution and increased biological effectiveness. Following high-LET IR, localized energy deposition along the particle trajectories induces clustered DNA lesions, leading to low electron density domains (LEDDs). To investigate the spatiotemporal dynamics of DNA repair and chromatin remodeling, we established the automated image analysis of transmission electron micrographs. Methods: Human fibroblasts were irradiated with high-LET carbon ions or low-LET photons. At 0.1 h, 0.5 h, 5 h, and 24 h post-IR, nanoparticle-labeled repair factors (53BP1, pKu70, pKu80, DNA-PKcs) were visualized using transmission electron microscopy in interphase nuclei to monitor the formation and repair of DNA damage in the chromatin ultrastructure. Using AI-based software tools, advanced image analysis techniques were established to assess the DNA damage pattern following low-LET versus high-LET IR. Results: Low-LET IR induced single DNA lesions throughout the nucleus, and most DNA double-strand breaks (DSBs) were efficiently rejoined with no visible chromatin decondensation. High-LET IR induced clustered DNA damage concentrated along the particle trajectories, resulting in circumscribed LEDDs. Automated image analysis was used to determine the exact number of differently sized nanoparticles, their distance from one another, and their precise location within the micrographs (based on size, shape, and density). Chromatin densities were determined from grayscale features, and nanoparticles were automatically assigned to euchromatin or heterochromatin. High-LET IR-induced LEDDs were delineated using automated segmentation, and the spatial distribution of nanoparticles in relation to segmented LEDDs was determined. Conclusions: The results of our image analysis suggest that high-LET IR induces chromatin relaxation along particle trajectories, enabling the critical repair of successive DNA damage. Following exposure to different radiation qualities, automated image analysis of nanoparticle-labeled DNA repair proteins in the chromatin ultrastructure enables precise characterization of specific DNA damage patterns

Optimal control of Allen-Cahn systems

Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented

Efficient Identification of HIV Serodiscordant Couples by Existing HIV Testing Programs in South Brazil.

ObjectiveTo examine the feasibility of identifying HIV negative at risk individuals in HIV serodiscordant couples, during voluntary HIV testing in South Brazil.MethodsWe surveyed HIV testers at 4 public testing sites in Rio Grande do Sul. We obtained information on risk behaviors and sexual partnerships. HIV testing and testing for recent infection were performed; HIV prevalence and risk behaviors were assessed among subjects who reported having a steady partner who was HIV positive (serodiscordant group) and compared with the general testing population.ResultsAmong 3100 patients, 490 (15.8%) reported being in a steady relationship with an HIV positive partner. New HIV infections were diagnosed in 23% of the serodiscordant group (vs. 13% in the general population, p = 0.01); among newly positive subjects, recent HIV infections were more frequent (23/86, 26.7%) among testers with positive partners than among the general testing group (52/334; 15.6%; p = 0.016). Less than half of the serodiscordant testers reported having used a condom during the last sexual intercourse with their HIV-positive partner. Participants with inconsistent condom use with steady partner were four times more likely to test positive for HIV compared to those who reported always using condoms with the steady partner (OR: 4.2; 95% CI: 2.3 to 7.5).ConclusionIt is highly feasible to identify large numbers of HIV susceptible individuals who are in HIV serodiscordant relationships in South Brazil testing sites. Condom use within HIV serodiscordant couples is low in this setting, suggesting urgent need for biomedical prevention strategies to reduce HIV transmission

Sharp interface limit for a phase field model in structural optimization

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of T-convergence of the reduced objective functional. Additionally, convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems