Optimal shape and location of sensors or actuators in PDE models

We investigate the problem of optimizing the shape and location of sensors and actuators for evolution systems driven by distributed parameter systems or partial differential equations (PDE). We consider wave, Schrödinger and heat equations on an arbitrary domain Ω, in any space dimension, and with suitable boundary conditions (if there is a boundary) which can be of Dirichlet, Neumann, mixed or Robin type. This kind of problem is frequently encountered in applications where one aims, for instance, at maximizing the quality of reconstruction of the solution, using only a partial observation. From the mathematical point of view, using probabilistic considerations we model this problem as that of maximizing the so-called randomized observability constant, over all possible subdomains of Ω having a prescribed measure. The spectral analysis of this problem reveals intimate connections with the theory of quantum chaos. More precisely, we provide a solution to this problem when the domain Ω satisfies suitable quantum ergodicity assumptions

Complexity and regularity of maximal energy domains for the wave equation with fixed initial data

We consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the restriction of the corresponding solution to ω over a time interval [0, T], over all possible subsets of Ω having a certain prescribed measure. We prove that this problem always has at least one solution and that, if the initial data satisfy some analyticity assumptions, then the optimal set is unique and moreover has a finite number of connected components. In contrast, we construct smooth but not analytic initial conditions for which the optimal set is of Cantor type and in particular has an infinite number of connected components

Optimal location of controllers for the one-dimensional wave equation

In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in L2(0,T;L2(ω)) steering the system exactly to zero. In this article we consider two optimal design problems. Let L∈(0,1). The first problem is to determine the optimal shape and position of ω in order to minimize the norm of the control for given initial data, over all possible measurable subsets ω of [0,π] of Lebesgue measure Lπ. The second problem is to minimize the norm of the control operator, over all such subsets. Considering a relaxed version of these optimal design problems, we show and characterize the emergence of different phenomena for the first problem depending on the choice of the initial data: existence of optimal sets having a finite or an infinite number of connected components, or nonexistence of an optimal set (relaxation phenomenon). The second problem does not admit any optimal solution except for L=1/2. Moreover, we provide an interpretation of these problems in terms of a classical optimal control problem for an infinite number of controlled ordinary differential equations. This new interpretation permits in turn to study modal approximations of the two problems and leads to new numerical algorithms. Their efficiency will be exhibited by several experiments and simulations

The design of CO2-based working fluids for high-temperature heat source power cycles

The application of CO2power cycles is advantageous to exploit high-temperature sources (500-800°C) in the case of available low-temperature heat sinks (15-25°C). However, their efficiency is strongly reduced for higher heat sink temperatures. At these temperatures, due to the low-critical temperature of CO2(about 31°C), CO2is in fact compressed in the supercritical vapor phase rather than in the liquid phase, thus increasing energetic demand for compression. One of the solutions envisaged to overcome this problem is the addition of one or more chemicals that allow having a mixture with a higher critical temperature than the one of pure CO2. This preserve the working fluid compression in its liquid phase, even in the case of heat sinks with temperatures greater than 25°C. This research shows that the addition to CO2of a properly selected chemical component enables to increase the critical temperature up to 45°C with relevant improvements of cycle efficiency with respect to pure-CO2power cycles. In particular, it summarizes the most relevant criteria to be accounted for when selecting CO2-additives. Moreover, the paper warns of the thermodynamic effects deriving from adding to CO2a second characterized by a much more high critical temperature, such as the occurrence of infinite-pressure critical points and multiple-phase liquid-liquid and vapor-liquid critical points. Finally, the paper analyses the thermodynamic properties of a high-critical temperature CO2-based mixture, suitable for these applications, that presents multiple phase critical points. In this regard, it is specified that the paper also aims at filling a knowledge gap in the study of thermodynamic properties of mixtures presenting how do enthalpy and specific volume change in response to pressure variations in the event of liquid-liquid and vapour-liquid critical points. Finally, we present the comparison between performances of power cycles which use, as working fluid, either pure CO2or the novel designed higher temperature CO2-based mixture

Not all features are created equal: Processing asymmetries between location and object features

Previous research has shown spontaneous location processing when location is not a task relevant feature and when a target is presented together with distractors. The present study investigates whether such processing can occur in the absence of distractor inhibition, and whether there is a processing asymmetry between location and an object feature. The results show that not all features are created equal. Whereas attending to an object’s color or texture led to the involuntary processing of that object’s location, attending to an object’s location did not necessarily result in the encoding of its color or texture when these nonspatial properties were not task relevant. These results add to the body of evidence demonstrating the special role of location in attentional selection. They also provide a clearer picture of the interactions among location, object features, and participants’ behavioral goals

What is the optimal shape of a pipe?

We consider an incompressible fluid in a three-dimensional pipe, following the Navier-Stokes system with classical boundary conditions. We are interested in the following question: is there any optimal shape for the criterion "energy dissipated by the fluid"? Moreover, is the cylinder the optimal shape? We prove that there exists an optimal shape in a reasonable class of admissible domains, but the cylinder is not optimal. For that purpose, we explicit the first order optimality condition, thanks to adjoint state and we prove that it is impossible that the adjoint state be a solution of this over-determined system when the domain is the cylinder. At last, we show some numerical simulations for that problem

Anatomical study of serotonergic innervation and 5-HT1A receptor in the human spinal cord

Serotonergic innervation of the spinal cord in mammals has multiple roles in the control of motor, sensory and visceral functions. In rats, functional consequences of spinal cord injury at thoracic level can be improved by a substitutive transplantation of serotonin (5-HT) neurons or regeneration under the trophic influence of grafted stem cells. Translation to either pharmacological and/or cellular therapies in humans requires the mapping of the spinal cord 5-HT innervation and its receptors to determine their involvement in specific functions. Here, we have performed a preliminary mapping of serotonergic processes and serotonin-lA (5-HT1A) receptors in thoracic and lumbar segments of the human spinal cord. As in rodents and non-human primates, 5-HT profiles in human spinal cord are present in the ventral horn, surrounding motoneurons, and also contact their presumptive dendrites at lumbar level. 5-HT1A receptors are present in the same area, but are more densely expressed at lumbar level. 5-HT profiles are also present in the intermediolateral region, where 5-HT1A receptors are absent. Finally, we observed numerous serotonergic profiles in the superficial part (equivalent of Rexed lamina II) of the dorsal horn, which also displayed high levels of 5-HT1A receptors. These findings pave the way for local specific therapies involving cellular and/or pharmacological tools targeting the serotonergic system

Evolution from syn-rift carbonates to early post-rift deep-marine intraslope lobes: The role of rift basin physiography on sedimentation patterns

The stratigraphic architecture of Early Jurassic strata exposed along a >10 km long transect in the Chachil Graben, an exhumed marine rift depocentre in the Neuquén Basin (Argentina), provides insights into the sedimentological and stratigraphic expression of the syn-rift to post-rift transition. A change from syn-rift intrabasinal carbonate to post-rift extrabasinal siliciclastic sedimentation is recorded, as well as variations in sediment supply and dispersal patterns across rift-related topography. The late syn-rift was marked by a transgression and development of a shallow-marine carbonate system, including carbonate platform deposits perched on fault-block highs and periplatform deposits accumulated in fault-block lows, which overlies continental volcano-sedimentary syn-rift deposits. Differential subsidence and basin deepening induced retrogradation of the carbonate system, which was progressively drowned and overlain by organic-rich calcareous mudstone that draped across rift structures at the onset of the early post-rift. The first extrabasinal siliciclastic influx led to progradation of an early post-rift intraslope lobe complex into the graben, which is associated with kilometre-scale clastic injectites. The depositional architecture, facies distribution and pinch-out style of intraslope lobes record the effects of an inherited compaction hinge, which acted as an oblique counterslope to sediment gravity flows. The occurrence of combined-flow bedforms, widespread erosion, and limited facies segregation across lobes bearing different hybrid event bed types, is in sharp contrast to sedimentological characteristics of existing intraslope lobe models. Documentation of the syn-rift to post-rift transition stratigraphy permitted identification of changes in thickness and facies resulting from the passive infill of inherited topography with early post-rift differential compaction. This architecture contrasts markedly with those developed during syn-rift normal faulting. Furthermore, the influence of local inherited topography on the development of early post-rift lobes is key to improve subsurface prediction of sandstone distribution and quality during assessment of hydrocarbon reservoirs and carbon storage sites

Stratigraphic change in flow transformation processes recorded in early post-rift deep-marine intraslope lobe complexes

The Early Jurassic Los Molles Formation in the Neuquén Basin of western Argentina is a rare example of well-exposed syn-rift to post-rift stratigraphy. In the Chachil Graben, the onset of the early post-rift stage is marked by drowning of a carbonate system and the development of two deep-marine intraslope lobe complexes. This field-based study in the Chachil Graben involved field mapping and correlating eleven stratigraphic logs, and petrographic analysis to document how grain size and texture within intraslope lobe sandstones change from the lobe centre to their frontal pinch-out. Eight different bed-scale facies are identified and inferred to be formed by turbulent (turbidites; Type A and B beds), transient turbulent–laminar (transitional flow deposits; Type C, D, E and F beds), laminar gravity flows (debrites; Type G) and post-depositional clastic injections (injectites; Type H beds). Fifteen lobes form two stacked lobe complexes that show stratigraphic evolution from a lower argillaceous sandstone-dominated lobe complex, built by transitional flow deposits, to an upper coarser-grained, sandier lobe complex largely constructed by turbidites. Petrographic analysis quantified sandstone mineralogy, matrix content, grain size and sorting, revealing that both lobe complexes are volcanic arc-sourced. This study proposes that the differences in the character of the two lobe complexes are due to maturation of sediment transport routes through progressive healing of the intraslope relief, with a concomitant decrease in substrate erosion and flow bulking. Also proposed here is a model for intraslope lobe complex development that accounts for the impact of flow-confinement on flow behaviour and transformation induced by the inherited topography. Bed type distribution suggests that high-density flows terminate more abruptly against confining slopes and produce greater depositional variability than lower-density flows. This integrated petrographic, architectural and sedimentary process model provides new insights into how post-rift intraslope lobe systems may act as hydrocarbon reservoirs, aquifers and carbon storage sites

Isolation of mineralizing Nestin+ Nkx6.1+ vascular muscular cells from the adult human spinal cord

<p>Abstract</p> <p>Background</p> <p>The adult central nervous system (CNS) contains different populations of immature cells that could possibly be used to repair brain and spinal cord lesions. The diversity and the properties of these cells in the human adult CNS remain to be fully explored. We previously isolated Nestin⁺Sox2⁺neural multipotential cells from the adult human spinal cord using the neurosphere method (i.e. non adherent conditions and defined medium).</p> <p>Results</p> <p>Here we report the isolation and long term propagation of another population of Nestin⁺cells from this tissue using adherent culture conditions and serum. QPCR and immunofluorescence indicated that these cells had mesenchymal features as evidenced by the expression of Snai2 and Twist1 and lack of expression of neural markers such as Sox2, Olig2 or GFAP. Indeed, these cells expressed markers typical of smooth muscle vascular cells such as Calponin, Caldesmone and Acta2 (Smooth muscle actin). These cells could not differentiate into chondrocytes, adipocytes, neuronal and glial cells, however they readily mineralized when placed in osteogenic conditions. Further characterization allowed us to identify the Nkx6.1 transcription factor as a marker for these cells. Nkx6.1 was expressed in vivo by CNS vascular muscular cells located in the parenchyma and the meninges.</p> <p>Conclusion</p> <p>Smooth muscle cells expressing Nestin and Nkx6.1 is the main cell population derived from culturing human spinal cord cells in adherent conditions with serum. Mineralization of these cells in vitro could represent a valuable model for studying calcifications of CNS vessels which are observed in pathological situations or as part of the normal aging. In addition, long term propagation of these cells will allow the study of their interaction with other CNS cells and their implication in scar formation during spinal cord injury.</p