Shedding Light on Diatom Photonics by means of Digital Holography

Diatoms are among the dominant phytoplankters in the worl's ocean, and their external silica investments, resembling artificial photonics crystal, are expected to play an active role in light manipulation. Digital holography allowed studying the interaction with light of Coscinodiscus wailesii cell wall reconstructing the light confinement inside the cell cytoplasm, condition that is hardly accessible via standard microscopy. The full characterization of the propagated beam, in terms of quantitative phase and intensity, removed a long-standing ambiguity about the origin of the light. The data were discussed in the light of living cell behavior in response to their environment

RBF approximation of large datasets by partition of unity and local stabilization

We present an algorithm to approximate large dataset by Radial Basis Function (RBF) techniques. The method couples a fast domain decomposition procedure with a localized stabilization method. The resulting algorithm can efficiently deal with large problems and it is robust with respect to the typical instability of kernel methods

Weak measurement og the composite Goo-Haenchen shift in the critical region

By using a weak measurement technique, we investigated the interplay between the angular and lateral Goos-Haenchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Haenchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.Comment: 10 pages, 3 figure

A New Phase Time Formula for Opaque Barrier Tunneling

After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.Comment: 9 pages, 2 figure

Delay Time in Quaternionic Quantum Mechanics

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.Comment: 9 pages, 5 figure

Fine structure of the choroidal coat of the avian eye: Lymphatic vessels

PURPOSE: To clarify the fine structure of the avian choroid and thus help explain the mechanisms for normal and abnormal eye function and growth. METHODS: Eyes from normal chickens and from experimental chickens subjected to unilateral paracentesis were fixed either by perfusion or in situ, with or without post-fixation by microwave irradiation, and then processed for light and electron microscopic analysis. RESULTS: The avian choroid contains thin-walled lacunae, whose fine structure is identical to that of lymphatic vessels. The lacunae are much smaller toward the anterior chamber and the Schlemm's canal than posteriorly in the eye bulb. Large lacunae are situated primarily in the suprachoroidea, and their blind-ended capillary branches enter the choriocapillaris and the walls of large veins. The walls of the large veins contain villous structures that protrude into their lumina and are penetrated by thin lacunar branches and by side lines of the venous lumen. In normal chickens, the lacunae usually are devoid of blood cells. After paracentesis of the anterior eye chamber, the lacunae become filled with erythrocytes on the side that was operated on, but not on the contralateral side. CONCLUSIONS: The authors propose that the lacunae of the avian choroid represent a system of posterior short lymphatic vessels, which drain intraocular fluids directly into the eye's venous system, and that the villous structures are sites of communication between lacunae and veins. The demonstration of a choroidal lymphatic system opens new insights into the processes of fluid removal, control of intraocular pressure, and regulation of choroidal thickness in the avian eye under normal and experimental conditions

Solving simple quaternionic differential equations

The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of left/right acting quaternionic operators, we prove existence and uniqueness for quaternionic initial value problems, discuss the reduction of order for quaternionic homogeneous differential equations and extend to the non-commutative case the method of variation of parameters. We also show that the standard Wronskian cannot uniquely be extended to the quaternionic case. Nevertheless, the absolute value of the complex Wronskian admits a non-commutative extension for quaternionic functions of one real variable. Linear dependence and independence of solutions of homogeneous (right) H-linear differential equations is then related to this new functional. Our discussion is, for simplicity, presented for quaternionic second order differential equations. This involves no loss of generality. Definitions and results can be readily extended to the n-order case.Comment: 9 pages, AMS-Te

Bulk and surface biaxiality in nematic liquid crystals

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially-varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor \Sb=(\grad \nn)(\grad \nn)^T possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor \QQ is induced to break the uniaxial symmetry about the director \nn. We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor become biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures

Quaternionic Diffusion by a Potential Step

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.Comment: 10 pages, 1 figur

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page