scholarly journals Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani
Keyword(s):  
Besov Space ◽  
Internal Control ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Critical Role ◽  
Boussinesq System ◽  
Heat Equations ◽  
Fluid Equation ◽  
Low Regularity ◽  
Finite Dimensional

Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega . Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} . The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1. The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d . Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution. Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Asymptotic velocity for four celestial bodies

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170426
Author(s):  
Andreas Knauf
Keyword(s):  
Celestial Mechanics ◽  
Integrable Systems ◽  
Energy Surface ◽  
Initial Conditions ◽  
Theme Issue ◽  
Asymptotic Velocity ◽  
Pair Potentials ◽  
Finite Dimensional ◽  
Celestial Bodies ◽  
Almost All

Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree − α for α ∈(0, 2), that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and almost all initial conditions on the energy surface. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

scholarly journals Significance of Nonsimilar Numerical Simulations in Forced Convection from Stretching Cylinder Subjected to External Magnetized Flow of Sisko Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jifeng Cui ◽  
Umer Farooq ◽  
Ahmed Jan ◽  
Murtada K. Elbashir ◽  
Waseem Asghar Khan ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Frictional Heating ◽  
Fluid Velocity ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Axial Direction ◽  
High Viscosity ◽  
Heat Equations ◽  
Dimensionless Numbers ◽  
Sisko Fluid

The practice of flowing effort is participating in various industries especially in nutrition productions all around the world. These fluids practices are utilized extensively in nutrition handling productions by making use of sticky liquids to produce valuable food manufactured goods in bulk. Nevertheless, such productions ought to guarantee that involved equipment such as pipelines are maintained clean as well as are cleared out for the efficient movement of fluids. The nonsimilar characteristics of involuntary convection from circular cylinder stretching in the axial direction subjected to an external flow of Sisko fluid characterized by the freely growing boundary layers (BL) are presented in this research. A circular cylinder is submerged in a stationary fluid. The axial stretching of the cylinder causes external fluid flow. The magnetic force of strength ″ B 0 ″ is enforced in the transverse direction. Because of the fluid's high viscosity, frictional heating due to viscous dissipation is quite significant. The flow is three dimensional but with no circumferential variations. The governing equations for axisymmetric flow that include the mass balance, x -momentum, and heat equation are modeled through conservation laws. The dimensionless system is developed by employing appropriate nonsimilar transformations. The numerical analyses are presented by adapting local nonsimilarity via finite-difference (FDM)-based MATLAB algorithm bvp4c. The characteristics of dimensionless numbers are determined by graphs that are plotted on momentum and heat equations. The nonsimilar simulations have been compared with the existing local similar solutions. Fluid velocity is increased as the material and curvature parameters are increased, resulting in improved heat transfer. The deviation in skin friction and local Nusselt number against the various dimensionless numbers is also analyzed.

Backward Mapping Methodology for Design Synthesis

1999 ◽  
Author(s):  
Stephen C.-Y. Lu ◽  
Satish T. S. Bukkapatnam ◽  
Ping Ge ◽  
Nanxin Wang
Keyword(s):  
Engineering Design ◽  
Design Space ◽  
Initial Conditions ◽  
Early Stage ◽  
Critical Role ◽  
Product Development Process ◽  
Engineering System ◽  
Design Synthesis ◽  
Performance Space ◽  
Backward Mapping

Abstract Design efficiency and robustness at early stage of parametric engineering design play a critical role in reducing cycle time and improving product quality in the overall product development process. Usually, the “forward mapping” approach, is used to find designs, where the desirable performances are satisfied through large iterations of analysis and evaluation from design space to performance space. However, these approaches are time-consuming and involve blind search if the engineering system simulation models and/or initial conditions are not appropriately selected. On the other hand, common “reverse engineering” methods use domain-specific assumptions and are not effective in generic scenarios where the presumed conditions are violated. In this paper, a Backward Mapping Methodology for Design Synthesis (BMDS) is presented that can help conduct design synthesis rapidly and robustly at early stage of parametric engineering design. BMDS is a surrogate model-based approach that combines the strengths of metamodeling and statistics. It can help designers explicitly identify the robust design solutions that satisfy the designer-specified performance requirements through a “backward mapping” from the performance space directly to the design space. Preliminary case studies show its effectiveness and potential to be used as a generic early stage parametric design synthesis methodology in the future.

Solving linear systems from dynamical energy analysis - using and reusing preconditioners

2021 ◽  
Vol 263 (5) ◽  
pp. 1041-1052
Author(s):  
Martin Richter ◽  
Gregor Tanner ◽  
Bruno Carpentieri ◽  
David J. Chappell
Keyword(s):  
Wave Equations ◽  
Energy Analysis ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solvers ◽  
Computational Method ◽  
Computational Time ◽  
Shell Elements ◽  
Finite Dimensional ◽  
Large Matrix

Dynamical energy analysis (DEA) is a computational method to address high-frequency vibro-acoustics in terms of ray densities. It has been used to describe wave equations governing structure-borne sound in two-dimensional shell elements as well as three-dimensional electrodynamics. To describe either of those problems, the wave equation is reformulated as a propagation of boundary densities. These densities are expressed by finite dimensional approximations. All use-cases have in common that they describe the resulting linear problem using a very large matrix which is block-sparse, often real-valued, but non-symmetric. In order to efficiently use DEA, it is therefore important to also address the performance of solving the corresponding linear system. We will cover three aspects in order to reduce the computational time: The use of preconditioners, properly chosen initial conditions, and choice of iterative solvers. Especially the aspect of potentially reusing preconditioners for different input parameters is investigated.

Chronic intrauterine pulmonary hypertension decreases calcium-sensitive potassium channel mRNA expression

2000 ◽  
Vol 279 (5) ◽  
pp. L857-L862 ◽  
Author(s):  
David N. Cornfield ◽  
Ernesto R. Resnik ◽  
Jean M. Herron ◽  
Steven H. Abman
Keyword(s):  
Gene Expression ◽  
Pulmonary Hypertension ◽  
Mrna Expression ◽  
Internal Control ◽  
Vascular Reactivity ◽  
Ductus Arteriosus ◽  
Critical Role ◽  
Mrna Levels ◽  
Channel Gene ◽  
Mrna Content

Calcium-sensitive potassium (KCa) channels play a critical role in mediating perinatal pulmonary vasodilation. Because infants with persistent pulmonary hypertension of the newborn (PPHN) have blunted vasodilator responses to birth-related stimuli, we hypothesized that lung KCachannel gene expression is decreased in PPHN. To test this hypothesis, we measured KCa channel gene expression in distal lung homogenates from both fetal lambs with severe pulmonary hypertension caused by prolonged compression of the ductus arteriosus and age-matched, sham-operated animals (controls). After at least 9 days of compression of the ductus arteriosus, fetal lambs were killed. To determine lung KCa channel mRNA levels, primers were designed against the known sequence of the KCa channel and used in semiquantitative RT-PCR, with lung 18S rRNA content as an internal control. Compared to that in control lambs, lung KCa channel mRNA content in the PPHN group was reduced by 26 ± 6% ( P < 0.02), whereas lung voltage-gated K+ 2.1 mRNA content was unchanged. We conclude that lung KCa channel mRNA expression is decreased in an ovine model of PPHN. Decreased KCa channel gene expression may contribute to the abnormal pulmonary vascular reactivity associated with PPHN.

scholarly journals Optimal anticipatory control as a theory of motor preparation: a thalamo-cortical circuit model

2020 ◽  
Author(s):  
Ta-Chu Kao ◽  
Mahdieh S. Sadabadi ◽  
Guillaume Hennequin
Keyword(s):  
Internal Control ◽  
Initial Conditions ◽  
Motor Preparation ◽  
Anticipatory Control ◽  
Subsequent Evolution ◽  
Population Activity ◽  
Prospective Control ◽  
Cortical Circuit ◽  
Low Dimensional ◽  
Low Dimensional Dynamics

SummaryAcross a range of motor and cognitive tasks, cortical activity can be accurately described by low-dimensional dynamics unfolding from specific initial conditions on every trial. These “preparatory states” largely determine the subsequent evolution of both neural activity and behaviour, and their importance raises questions regarding how they are — or ought to be — set. Here, we formulate motor preparation as optimal prospective control of future movements. The solution is a form of internal control of cortical circuit dynamics, which can be implemented as a thalamo-cortical loop gated by the basal ganglia. Critically, optimal control predicts selective quenching of variability in components of preparatory population activity that have future motor consequences, but not in others. This is consistent with recent perturbation experiments performed in mice, and with our novel analysis of monkey motor cortex activity during reaching. Together, these results suggest optimal anticipatory control of movement.

scholarly journals THE THEOREM OF AVERAGING IN THE CONDITION OF UNLIMETED SPEED FOR ALMOST-PERIODIC FUNCTIONS

2017 ◽  
Vol 19 (3) ◽  
pp. 53-57
Author(s):  
O.P. Filatov
Keyword(s):  
Differential Inclusion ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Almost Periodic ◽  
Independent Variables ◽  
Finite Dimensional ◽  
All Solutions ◽  
Independent Variable ◽  
The Right

It is proved that the limit of maximal mean is an independent variable of initial conditions if an axis exists from the convex hull of a set of permitted speeds out of a finite-dimensional space and the components of direction vector of the axis are the independent variables with respect to a spectrum of almost-periodic function. The set of permitted speeds is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.

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