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Register a new userRapid Transport of Glassy Supersolid Helium in Wavy-Rough Nanpores
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Zotin K.-H. Chu
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We show that the presumed wavy roughness distributed along the wall of different nanopores (radius : a around 3.5 nm for Vycor or a silica glass; around 245 nm for porous gold) will induce larger volume flow rates of solid helium (of which there is a minimum) which might explain reported experimental differences of the supersolid fractions observed so far.
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Glassy matter, as subjected to high shear rates, exhibit shear thinning : i.e., the viscosity diminishes with increasing shear rate. Meanwhile one prominent difference between the transport in micropores and that in macroscale is the (relatively) larger roughness observed inside micropores. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the transport in micropores. By treating the glass as a shear-thinning matter and using the rate-dependent model together with the boundary perturbation method, we can analytically obtain the transport results up to the second order.
The deformation kinetics for glassy solid helium confined in microscopic domain at very low temperature regime was investigated using a transition-rate model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be nearly frictionless fields for rate of deformation due to the almost vanishing shear stress in microtubes at very low temperature regime subjected to some surface conditions : The relatively larger roughness (compared to the macroscopic domain) inside microtubes and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the deformation kinetics in microtubes. By using the boundary perturbation method, we obtained a class of temperature and activation energy dependent fields for the deformation kinetics at low temperature regime with the presumed small wavy roughness distributed along the walls of an cylindrical microtube. The critical deformation kinetics of the glassy matter is dependent upon the temperature, activation energy, activation volume, orientation dependent and is proportional to the (referenced) shear rate, the slip length, the amplitude and the orientation of the wavy-roughness. Finally, we also discuss the quantitative similarity between our results with Ray and Hallock [Phys. Rev. Lett. {bf 100}, 235301 (2008)].
We obtain the approximate solutions for the steady temperature profiles of materials with a temperature-dependent thermal absorptivity inside a microannulus with wavy-rough surfaces considering a quasilinear partial differential equation by the boundary perturbation approach. We found the critical Frank-Kamanestkii parameter will depend on the small amplitude wavy-roughness.
We consider Dirac particles confined to a thin strip, e.g., graphene nanoribbon, with rough edges. The confinement is implemented by a large mass in the Hamiltonian or by imposing boundary conditions directly on the graphene wave-functions. The scattering of a rough edge leads to a transverse channel-mixing and provides crucial limitation to the quantum transport in narrow ribbons. We solve the problem perturbatively and find the edge scattering contribution to the conductivity, which can be measured experimentally. The case of Schroedinger particles in a strip is also addressed, and the comparison between Schroedinger and Dirac transport is made. Anomalies associated with quasi-one dimensionality, such as Van Hove singularities and localization, are discussed. The violation of the Matthiessen rule is pointed out.
This paper will deal with the modeling-problem of combining thermal subsystems (e.g. a semiconductor module or package with a cooling radiator) making use of reduced models. The subsystem models consist of a set of Foster-type thermal equivalent circuits, which are only behavioral models. A fast al-gorithm is presented for transforming the Foster-type circuits in Cauer-circuits which have physical behavior and therefore allow for the construction of the thermal model of the complete system. Then the set of Cauer-circuits for the complete system is transformed back into Foster-circuits to give a simple mathematical representation and applicability. The transfor-mation algorithms are derived in concise form by use of recur-sive relations. The method is exemplified by modeling and measurements on a single chip IGBT package mounted on a closed water cooled radiator. The thermal impedance of the complete system is constructed from the impedances of the sub-systems, IGBT-package and radiator, and also the impedance of the package can be inferred from the measured impedance of the complete system.
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