Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

Effect of acute copper sulfate exposure on olfactory responses to amino acids and pheromones in goldfish (Carassius auratus)

Exposure of olfactory epithelium to environmentally relevant concentrations of copper disrupts olfaction in fish. To examine the dynamics of recovery at both functional and morphological levels after acute copper exposure, unilateral exposure of goldfish olfactory epithelia to 100 μM CuSO4 (10 min) was followed by electro-olfactogram (EOG) recording and scanning electron microscopy. Sensitivity to amino acids (L-arginine and L-serine), generally considered food-related odorants, recovered most rapidly (three days), followed by that to catecholamines(3-O-methoxytyramine),bileacids(taurolithocholic acid) and the steroid pheromone, 17,20 -dihydroxy-4-pregnen- 3-one 20-sulfate, which took 28 days to reach full recovery. Sensitivity to the postovulatory pheromone prostaglandin F2R had not fully recovered even at 28 days. These changes in sensitivity were correlated with changes in the recovery of ciliated and microvillous receptor cell types. Microvillous cells appeared largely unaffected by CuSO4 treatment. Cilia in ciliated receptor neurones, however, appeared damaged one day post-treatment and were virtually absent after three days but had begun to recover after 14 days. Together, these results support the hypothesis that microvillous receptor neurones detect amino acids whereas ciliated receptor neurones were not functional and are responsible for detection of social stimuli (bile acidsandpheromones).Furthermore, differences in sensitivity to copper may be due to different transduction pathways in the different cell types

Holographic renormalization as a canonical transformation

The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equations of motion that inherits a well defined symplectic form from that on phase space. The requirement of a well defined symplectic form is essential and often leads to a necessary repackaging of the degrees of freedom. (ii) Once the space of asymptotic solutions has been constructed in terms of the correct degrees of freedom, then there exists a boundary term that is obtained as a certain solution of the Hamilton-Jacobi equation which simultaneously makes the variational problem well defined and preserves the symplectic form. This procedure is identical to holographic renormalization in the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a footnote on Palatini gravity added. Version to appear in JHE

Kirchhoff's Rule for Quantum Wires

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with $n$ channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy $E>0$ is explicitly given in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory. Finally we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs only use known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitean symplectic forms.Comment: 40 page

Quantum Cosmology of Generalized Two--Dimensional Dilaton Gravity Models

The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding Wheeler-DeWitt equation are presented. A wider class of minisuperspace models that can be solved in this fashion is identified. Supersymmetric extensions to the induced gravity theory and the bosonic string theory are then considered and closed-form solutions to the associated quantum constraints are derived. The possibility of applying the third-quantization procedure to two-dimensional dilaton-gravity is briefly discussed.Comment: 28 pages, late

Extension of Murray's law using a non-Newtonian model of blood flow

<p>Abstract</p> <p>Background</p> <p>So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.</p> <p>Modeling</p> <p>In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. Σ<it>R</it>^{<it>c </it>}= <it>cste </it>with <it>c </it>= 3 is verified and is independent of <it>n</it>, the dimensionless index in the viscosity equation; <it>R </it>being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of <it>c </it>may be calculated depending on the value of <it>n</it>.</p> <p>Results</p> <p>We find that <it>c </it>varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to <it>c </it>= 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.</p> <p>Conclusion</p> <p>It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.</p

An analytical approach for prediction of elastohydrodynamic friction with inlet shear heating and starvation

An analytical friction model is presented, predicting the coefficient of friction in elastohydrodynamic (EHD) contacts. Three fully formulated SAE 75W-90 axle lubricants are examined. The effect of inlet shear heating (ISH) and starvation is accounted for in the developed friction model. The film thickness and the predicted friction are compared with experimental measurements obtained through optical interferometry and use of a mini traction machine. The results indicate the significant contribution of ISH and starvation on both the film thickness and coefficient of friction. A strong interaction between those two phenomena is also demonstrated, along with their individual and combined contribution on the EHD friction