Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from nondestructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem.We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential illposedness, the stability estimate obtained is optimal

A Strategy for Passive Control of Natural Roll-Waves in Power-Law Fluids through Inlet Boundary Conditions

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Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis

The paper investigates the applicability of Kinematic and Diffusive Wave models for mud-flows with a power-law shear-thinning rheology. In analogy with a well-known approach for turbulent clear-water flows, the study compares the steady flow depth profiles predicted by approximated models with those of the Full Dynamic Wave one. For all the models and assuming an infinitely wide channel, the analytical solution of the flow depth profiles, in terms of hypergeometric functions, is derived. The accuracy of the approximated models is assessed by computing the average, along the channel length, of the errors, for several values of the Froude and kinematic wave numbers. Assuming the threshold value of the error equal to 5%, the applicability conditions of the two approximations have been individuated for several values of the power-law exponent, showing a crucial role of the rheology. The comparison with the clear-water results indicates that applicability criteria for clear-water flows do not apply to shearthinning fluids, potentially leading to an incorrect use of approximated models if the rheology is not properly accounted for

Impact dynamics of mud flows against rigid walls

Mud flows represent one of the major causes of natural hazards in mountain regions. Similarly to debris flows, they consist of a hyper-concentrated mixture of water and sediments flowing down a slope and may cause serious damages to people and structures. The present paper investigates the force produced by a dam-break wave of mud impacting against a rigid wall. A power-law shearthinning model is used to describe the rheology of the hyper-concentrated mixture. A onedimensional shallow water model is adopted and a second-order Finite Volume scheme is employed to numerically solve the governing equations. The results indicate that depending on the fluid rheological parameters and on the bottom slope, there exists a minimum value of the wall distance above which the peak force does not exceed the asymptotic value of the hydrostatic final condition. For two different values of the channel slope, the dimensionless value of this lower bound is individuated for several values of the power-law exponent and of a dimensionless Basal Drag coefficient. An estimation of the maximum peak force for wall distance smaller than the minimum value is also provided

Exponential instability for inverse elliptic problems with unknown boundaries

We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed

Neural cell adhesion molecule-mediated fyn activation promotes GABAergic synapse maturation in postnatal mouse cortex

GABAergic basket interneurons form perisomatic synapses, which are essential for regulating neural networks, and their alterations are linked to various cognitive dysfunction. Maturation of basket synapses in postnatal cortex is activity dependent. In particular, activity-dependent downregulation of polysialiac acid carried by the neural cell adhesion molecule (NCAM) regulates the timing of their maturation. Whether and how NCAM per se affects GABAergic synapse development is unknown. Using single-cell genetics to knock out NCAM in individual basket interneurons in mouse cortical slice cultures, at specific developmental time periods, we found that NCAM loss during perisomatic synapse formation impairs the process of basket cell axonal branching and bouton formation. However, loss of NCAM once the synapses are already formed did not show any effect. We further show that NCAM120 and NCAM140, but not the NCAM180 isoform, rescue the phenotype. Finally, we demonstrate that a dominant-negative form of Fyn kinase mimics, whereas a constitutively active form of Fyn kinase rescues, the effects of NCAM knockdown. Altogether, our data suggest that NCAM120/NCAM140-mediated Fyn activation promotes GABAergic synapse maturation in postnatal cortex

Influence of bed morphology on double-averaged turbulent quantities in low submergence gravel-bed flows

River hydrodynamicsTurbulent open channel flow and transport phenomen