Nonlinear modal analysis of an L-shape beam structure

In this work it is derived the nonlinear equations of motion of L-shaped beam structure considering rotary inertia terms for out-of-plane motion in order to be used for nonlinear modal analysis of the structure. The dynamics has been projected in the infinite mode shapes space and it is derived the equations of motion in generalized coordinates. The nonlinear equations of motion indicates that there is coupling between in-plane and out-of-plane motions which in linear case is not the case

Linear modal analysis of L-shaped beam structures

In this article a theoretical linear modal analysis of Euler-Bernoulli L-shaped beam structures is performed by solving two sets of coupled partial differential equations of motion. The first set, with two equations, corresponds to in-plane bending motions whilst the second set with four equations corresponds to out-of-plane motions with bending and torsion. The case is also shown of a single cantilever beam taking into account rotary inertia terms. At first for the case of examination of the results for the L-shaped beam structure, an individual modal analysis is presented for four selected beams which will be used for modelling an L-shaped beam structure; in order to investigate the influence of rotary inertia terms and shear effects. Then, a theoretical and numerical modal analysis is performed for four models of the L-shaped beam structure consisting of two sets of beams, in order to examine the effect of the orientation of the secondary beam (oriented in two ways) and also shear effects. The comparison of theoretical and finite element simulations shows a good agreement for both in-plane and out-of-plane motions, which validates the theoretical analysis. This work is essential to make progress with new investigations into the nonlinear equations for the L-shaped beam structures within Nonlinear Normal Mode theory

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation (SFG) with entangled photon-pairs, generating as many as 40,000 SFG photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity-dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach is readily applicable for other nonlinear interactions, and may be applicable for various quantum-measurement tasks.Comment: 4 pages, 2 figures, Accepted to Phys. Rev. Let

Towards linear modal analysis for an L-shaped beam: equations of motion

We consider an L-shaped beam structure and derive all the equations of motion considering also the rotary inertia terms. We show that the equations are decoupled in two motions, namely the in-plane bending and out-of-plane bending with torsion. In neglecting the rotary inertia terms the torsional equation for the secondary beam is fully decoupled from the other equations for out-of-plane motion. A numerical modal analysis was undertaken for two models of the L-shaped beam, considering two different orientations of the secondary beam, and it was shown that the mode shapes can be grouped into these two motions: in-plane bending and out-of-plane motion. We compared the theoretical natural frequencies of the secondary beam in torsion with finite element results which showed some disagreement, and also it was shown that the torsional mode shapes of the secondary beam are coupled with the other out-of-plane motions. These findings confirm that it is necessary to take rotary inertia terms into account for out-of-plane bending. This work is essential in order to perform accurate linear modal analysis on the L-shaped beam structure

Delta-like and gtl2 are reciprocally expressed, differentially methylated linked imprinted genes on mouse chromosome 12

AbstractThe distal portion of mouse chromosome 12 is imprinted. To date, however, Gtl2 is the only imprinted gene identified on chromosome 12. Gtl2 encodes multiple alternatively spliced transcripts with no apparent open reading frame. Using conceptuses with maternal or paternal uniparental disomy for chromosome 12 (UPD12), we found that Gtl2 is expressed from the maternal allele and methylated at the 5′ end of the silent paternal allele. A reciprocally imprinted gene, Delta-like (Dlk), with homology to genes involved in the Notch signalling pathway was identified 80kb upstream of Gtl2. Dlk was expressed exclusively from the paternal allele in both the embryo and placenta, but the CpG-island promoter of Dlk was completely unmethylated on both parental alleles. Rather, a paternally methylated region was identified in the last exon of the active Dlk allele. The proximity, reciprocal imprinting and methylation in this domain are reminiscent of the co-ordinately regulated Igf2–H19 imprinted domain on mouse chromosome 7. Like H19 and Igf2, Gtl2 and Dlk were found to be co-expressed in the same tissues throughout development, though not after birth. These results have implications for the regulation, function and evolution of imprinted domains

Acoustic Physiology in Mosquitoes

The acoustic physiology of mosquitoes is perhaps the most complex within the entire insect class. Past research has uncovered several of its-sometimes stunningly unconventional-principles, but many mysteries remain. Their solution necessitates a concerted transdisciplinary effort to successfully link the neuroanatomical and biophysical properties of mosquito flagellar ears to the behavioral ecology of entire mosquito populations. Neuroanatomically, mosquito ears can rival those of humans in both complexity and sheer size. The approximately 16,000 auditory hair cells within the human organ of Corti, for example, are matched by the approximately 16,000 auditory neurons in the Johnston's organ of a male Anopheles mosquito. Both human and mosquito ears receive very extensive efferent innervation, which modulates their function in ways that are as yet poorly understood. Different populations of neuronal and nonneuronal cell types divide the labor of the mosquito ear amongst themselves. Yet, what exactly this labor is, and how it is achieved, is at best vaguely known. For the majority of mosquitoes, biologically relevant sounds are inextricably linked to their flight tones. Either these flight tones are (directly) the sounds of interest or they contribute (indirectly) to the production of audible sound through a process called nonlinear distortion. Finally, male ears can generate tones themselves: The generation of an internal "phantom copy" of a female flight tone (or self-sustained oscillation) is believed to aid the male hearing process. Here, we introduce protocols that target the mosquitoes' auditory neuroanatomy, electrophysiology, and behavior to help shed light on some of these issues

Teleportation of continuous quantum variables

A particularly startling discovery by Bennett et al. is the possibility for teleportation of a quantum state, whereby an unknown state of a spin-1/2 particle is transported by Alice from a sending station to Bob at a receiving terminal by conveying 2 bits of classical information. Beyond the context of dichotomic variables, Vaidman has analyzed teleportation of the wave function of a one-dimensional particle in a beautiful variation of the original EPR paradox. Here we extend Vaidman's analysis to incorporate finite (nonsingular) degrees of correlation among the relevant particles

Phase-dependent spectra in a driven two-level atom

We propose a method to observe phase-dependent spectra in resonance fluorescence, employing a two-level atom driven by a strong coherent field and a weak, amplitude-fluctuating field. The spectra are similar to those which occur in a squeezed vacuum, but avoid the problem of achieving squeezing over a $4\pi$ solid angle. The system shows other interesting features, such as pronounced gain without population inversion.Comment: 4 pages and 4 figures. Submitted to Phys. Rev. Let

Resonance fluorescence spectrum in a weak squeezed field with an arbitrary bandwidth

We analyze the linewidth narrowing in the fluorescence spectrum of a two-level atom driven by a squeezed vacuum field of a finite bandwidth. It is found that the fluorescence spectrum in a low-intensity squeezed field can exhibit a (omega - omega(0))(-6) frequency dependence in the wings. We show that this fast fall-off behavior is intimately related to the properties of a narrow-bandwidth squeezed field and does not extend into the region of broadband excitation. We apply the Linear response model and find that the narrowing results from a convolution of the atom response with the spectrum of the incident field. On the experimental side, we emphasize that the linewidth narrowing is not sensitive to the solid angle of the squeezed modes coupled to the atom. We also compare the fluorescence spectrum with the quadrature-noise spectrum and find that the fluorescence spectrum for an off-resonance excitation does not reveal the noise spectrum. We show that this difference arises from the competing three-photon scattering processes. [S1050-2947(98)04308-X]