Existence, Uniqueness and Convergence of Simultaneous Distributed-Boundary Optimal Control Problems

We consider a steady-state heat conduction problem $P$ for the Poisson equation with mixed boundary conditions in a bounded multidimensional domain $\Omega$. We also consider a family of problems $P_{\alpha}$ for the same Poisson equation with mixed boundary conditions being $\alpha>0$ the heat transfer coefficient defined on a portion $\Gamma_{1}$ of the boundary. We formulate simultaneous \emph{distributed and Neumann boundary} optimal control problems on the internal energy $g$ within $\Omega$ and the heat flux $q$, defined on the complementary portion $\Gamma_{2}$ of the boundary of $\Omega$ for quadratic cost functional. Here the control variable is the vector $(g,q)$. We prove existence and uniqueness of the optimal control $(\overline{\overline{g}},\overline{\overline{q}})$ for the system state of $P$, and $(\overline{\overline{g}}_{\alpha},\overline{\overline{q}}_{\alpha})$ for the system state of $P_{\alpha}$, for each $\alpha>0$, and we give the corresponding optimality conditions. We prove strong convergence, in suitable Sobolev spaces, of the vectorial optimal controls, system and adjoint states governed by the problems $P_{\alpha}$ to the corresponding vectorial optimal control, system and adjoint states governed by the problem $P$, when the parameter $\alpha$ goes to infinity. We also obtain estimations between the solutions of these vectorial optimal control problems and the solution of two scalar optimal control problems characterized by fixed $g$ (with boundary optimal control $\overline{q}$) and fixed $q$ (with distributed optimal control $\overline{g}$), respectively, for both cases $\alpha>0$ and $\alpha=\infty$.Comment: 14 page

Effect of Ceramic Scaffold Architectural Parameters on Biological Response.

Numerous studies have focused on the optimization of ceramic architectures to fulfill a variety of scaffold functional requirements and improve biological response. Conventional fabrication techniques, however, do not allow for the production of geometrically controlled, reproducible structures and often fail to allow the independent variation of individual geometric parameters. Current developments in additive manufacturing technologies suggest that 3D printing will allow a more controlled and systematic exploration of scaffold architectures. This more direct translation of design into structure requires a pipeline for design-driven optimization. A theoretical framework for systematic design and evaluation of architectural parameters on biological response is presented. Four levels of architecture are considered, namely (1) surface topography, (2) pore size and geometry, (3) porous networks, and (4) macroscopic pore arrangement, including the potential for spatially varied architectures. Studies exploring the effect of various parameters within these levels are reviewed. This framework will hopefully allow uncovering of new relationships between architecture and biological response in a more systematic way as well as inform future refinement of fabrication techniques to fulfill architectural necessities with a consideration of biological implications.The authors gratefully acknowledge the financial support of the Gates Cambridge Trust and Geistlich Pharma AG.This is the final version of the article. It first appeared from Frontiers via http://dx.doi.org/10.3389/fbioe.2015.0015

Numerical analysis of a family of simultaneous distributed-boundary mixed elliptic optimal control problems and their asymptotic behaviour through a commutative diagram and error estimates

In this paper, we consider a family of simultaneous distributed-boundary optimal control problems ($P_{\alpha}$) on the internal energy and the heat flux for a system governed by a mixed elliptic variational equality with a parameter $\alpha >0$ and a simultaneous distributed-boundary optimal control problem ($P$) governed also by an elliptic variational equality with a Dirichlet boundary condition on the same portion of the boundary. We formulate discrete approximations $\left(P_{h \alpha}\right)$ and $\left(P_h\right)$ of the problems $\left(P_\alpha\right)$ and $(P)$ respectively, for each $h>0$ and for each $\alpha>0$, through the finite element method with Lagrange's triangles of type 1 with parameter $h$ (the longest side of the triangles). The goal of this paper is to study the convergence of this family of discrete simultaneous distributed-boundary mixed elliptic optimal control problems $\left(P_{h \alpha}\right)$ when the parameters $\alpha$ goes to infinity and the parameter $h$ goes to zero simultaneously. We prove the convergence of the problems $\left(P_{h \alpha}\right)$ to the problem $\left(P_h\right)$ when $\alpha \rightarrow +\infty$, for each $h>0$. We study the convergence of the problems $\left(P_{h \alpha}\right)$ and $\left(P_h\right)$, for each $\alpha >0$, when $h \rightarrow 0^+$ obtaining a commutative diagram which relates the continuous and discrete optimal control problems $\left(P_{h \alpha}\right),\left(P_\alpha\right),\left(P_h\right)$ and $(P)$ by taking the limits $h \rightarrow 0^+$ and $\alpha \rightarrow +\infty$ respectively. We also study the double convergence of $\left(P_{h \alpha}\right)$ to $(P)$ when $(h, \alpha) \rightarrow(0^+,+\infty)$ which represents the diagonal convergence in the above commutative diagram.Comment: This paper has been published online in Nonlinear Analysis: Real World Applications. arXiv admin note: text overlap with arXiv:1512.0383

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.Comment: 22 page

Co-targeting the IGF system and HIF-1 inhibits migration and invasion by (triple-negative) breast cancer cells

BACKGROUND: Metastatic triple-negative breast cancer is mostly incurable, due to lack of suitable drug targets. The insulin-like growth factor (IGF) system could provide such a target, and IGF-1 receptor (IGF-1R)-directed agents are already available, but seem unable to control all the complexities of the system, including crosstalk with hypoxia-inducible pathways. METHODS: Migration of triple-negative MDA-231 breast cancer cells and its modulation by IGFs, the IGF-1R inhibitor NVP-AEW541 and the IGF-2-sequestering monoclonal antibody MAB292 were assessed by the scratch wound healing and Boyden chamber assays; the effect of topotecan (inhibiting hypoxia-inducible factor-1 (HIF-1)) under hypoxia was also evaluated. Constitutive as well as drug-modulated levels of components of the IGF and HIF-1 pathways were evaluated by western blotting and qPCR. RESULTS: IGF-induced migration of MDA-231 cells was not abrogated by the IGF-1R inhibitor NVP-AEW541, whereas IGF-2 sequestration by MAB292 significantly reduced cell migration. Under hypoxia, topotecan was also effective, likely by reducing HIF-1-induced IGF-2 release. Simultaneous targeting of IGF-1R and IGF-2 or HIF-1 completely abolished cell migration. CONCLUSIONS: IR activation may account for the failure of NVP-AEW541 to suppress MDA-231 cell migration. Ligand-targeting compounds, or co-inhibition of the IGF and HIF-1 systems, may prevent activation of compensatory signalling, thereby providing a valuable addition to IGF-1R inhibitor-based therapies

Critical assessment of thermal conductivity models for Miscibility Gap Alloy-based composite Phase Change Materials for high temperature Thermal Energy Storage

Miscibility Gap Alloys (MGAs), such as Al-Sn-based systems, provide a viable solution for the development of composite Phase Change Materials (PCMs) for Thermal Energy Storage (TES) purposes. Their successful production depends on the cooling rate imposed to the melt. Finite Element Analyses (FEA), which relies also on thermal conductivity values, represent a powerful tool for the design of the production process. Thermal conductivity, which depends on the arrangement of the phases in the system, also affects the thermal response of the alloy. In the view of evaluating the impact of the phase morphology, the authors adapted some of the models developed for composites and solutions to Al-Sn and Al-Sn-Si-Mg alloys, characterized by broad solidification ranges in terms of composition and temperature and by significantly different phases thermal conductivity. In the fully-liquid range, Filippov and Novoselova model was selected for the description of both alloys. Models that consider sphere-like dispersions give values quite close to the theoretical upper Wiener bound when the high-melting phase is solid. The phase morphology impact is relevant when the solidification range is considered. The resulting arrangement-related thermal conductivity curves are compared to those supplied by CALPHAD-based software and to available literature data

Experiência com símbolos e compreensão de desenhos em crianças pequenas de diferentes contextos socioeconómicos

The purpose of this research was to explore the relationships between children’s early comprehension of drawings in two socioeconomic groups (middle- and low-ses) and the experiences with symbols at home. Twenty-eight children between 30 and 38 months of age solved a matching task in which they had to relate five objects with their black-and-white line drawings; their mothers completed a questionnaire regarding the quantity and variety of pictures at home and the shared activities between adults and children with these symbols. The results show that only middle-SES children were able to understand the drawing-referent relation; symbolic performance was mainly associated with the presence of resources with children’s images at home (dvd and children’s books) and with adultchild interactions with these resources, such as joint experiences with audio-visual images, storytelling and maternal assistance when children draw. Keywords: Drawings, comprehension, symbolic experience, socioeconomic level.El propósito de esta investigación fue profundizar el estudio de la comprensión temprana de dibujos en niños de nivel socioeconómico medio (NSE medio) y bajo (NSE bajo) y examinar la influencia en este proceso de las experiencias con imágenes en el contexto familiar. Para ello, 28 niños de entre 30 y 38 meses resolvieron una tarea de correspondencias en la que debían establecer relaciones entre cinco objetos y sus dibujos en lápiz negro; sus madres contestaron un cuestionario sobre las experiencias infantiles con distintos tipos de imágenes (imágenes audiovisuales, fotografías y dibujos) y las prácticas entre adultos y niños con estas representaciones. Los resultados muestran que solamente los niños de NSE medio demostraron comprender la relación dibujo-referente; el desempeño simbólico se asoció principalmente con la presencia en los hogares de recursos con imágenes para niños (DVD y libros infantiles) y con las interacciones adulto-niño con estos recursos, como las experiencias conjuntas con imágenes audiovisuales, la lectura de cuentos y la asistencia materna al dibujar.    O propósito desta pesquisa foi explorar as relações entre a compreensão temporã de desenhos em crianças de nível socioeconómico meio (nse médio) e baixo (nse baixo) e as experiências 30 e 38 meses resolveram uma tarefa de correspondências na que deviam establecer relações entre cinco objetos e seus desenhos em lápiz preto; suas mães contestaram um questionário sobre a quantidade e a variedade de imagens nos lares e as atividades partilhadas por adultos e crianças cm estas representações. Os resultados mostram que só as crianças de nse médio demostraram compreender a relação desenho-referente; o desempenho simbólico associou-se principalmente com a presença nos lares de recursos com imagens para crianças (dvd e libros infantis) e com as interações adulto-criança com estes recursos, como as experiências conjuntas com imagensaudiovisuais, a leitura de livros e a assistência materna ao desenhar.Palavras-chave: desenhos, compreensão, experiencia simbólica, nível socioeconómico