187 research outputs found
Wave analysis of Airy beams and Airy Pulsed Beams
No full textThe Airy beam (AiB) has attracted a lot of attention recently because of its intriguing features. We have previously provided a cogent physical explanation for these properties by showing that the AiB is, in fact, a caustic of rays that radiate from the tail of the Airy function aperture distribution. We have also introduced a class of ultra wide band (UWB) Airy pulsed beams (AiPB), where a key step has been the use of a proper frequency scaling of the initial aperture field that ensures that all the frequency components propagate along the same curved trajectory so that the wavepacket of the AiPB does not disperse. An exact closed form solution for the AiPB has been derived using the spectral theory of transients (STT) which is an extension of the well know Cagniard\u96de Hoop (CdH) method. In this paper we discuss the properties of the AiB and AiPB, and use the present problem to discuss the relation between the CdH method and the STT
Discretised Airy stress functions and body forces
No full textThis paper extends polyhedral Airy stress functions to incorporate body forces. Stresses of an equilibrium state of a 2D structure can be represented by the sec- ond derivatives of a smooth Airy stress function and the integrals of body forces. In the absence of body forces, a smooth Airy stress function can be discretised into a polyhedron as the corresponding structure is discretised into a truss. The differ- ence in slope across a creases represents the axial force on the bar, while the zero curvatures of the planar faces represent zero stresses voids of the structure. When body forces are present, the zero-stress condition requires the discretised Airy stress function to curve with the integrals of these body forces. Meanwhile, the isotropic angles on the creases still indicate concentrated axial forces. This paper discretises the integrals of body forces into step-wise functions, and discretises the Airy stress function into quadric faces connected by curved creases. The proposed method could provide structural designers (e.g. architects, structural engineers) with a more intuitive way to perceive stress fields.Structural Design & Mechanic
The Gouy phase of Airy beams
Get PDFThe phase behavior of Airy beams is studied, and their Gouy phase is defined. Analytic expressions for the idealized, infinite-energy type beam are derived. They are shown to be excellent approximations for finite-energy beams generated under typical experimental conditions.TelecommunicationsElectrical Engineering, Mathematics and Computer Scienc
On the pitfalls of Airy isostasy and the isostatic gravity anomaly in general
Get PDFIsostatic gravity anomalies provide a measure of the Earth's gravity field free from the gravitational attractions of the topography and its isostatic compensation, most commonly represented by a variation in the depth of a compensating density contrast, for example the Moho. They are used by both geodesists and geophysicists alike, though often for different purposes. Unfortunately though, the effect of subsurface loading on the lithosphere renders transfer function (admittance) methods unusable when surface and subsurface loads coexist. Where they exist, subsurface loads are often expressed in the Bouguer anomaly but not in the topography, and it is shown here that this phase disconnect cannot be faithfully represented by either realor complex-valued analytic admittance functions. Additionally, many studies that employ the isostatic anomaly ignore the effects of the flexural rigidity of the lithosphere, most often represented as an effective elastic thickness (Te), and assume only Airy isostasy, i.e. surface loading of a plate with zero elastic thickness. The consequences of such an omission are studied here, finding that failure to account for flexural rigidity and subsurface loading can result in (1) over- or underestimates of both inverted Moho depths and dynamic topography amplitude, and (2) underestimates of the size of topographic load that can be supported by the plate without flexure. An example of the latter is shown over Europe. Finally, it is demonstrated how low values of the isostatic anomaly variance can actually be biased by these anomalies having low power at the long wavelengths while still possessing high power at middle to short wavelengths, compared to the corresponding Bouguer anomaly power spectrum. This will influence the choice of best-fitting isostatic model if the model is chosen by minimization of the isostatic anomaly standard deviation
Exponentially Reduced Reflection (ERR) versus Linear Wave Theory (Airy-Laplace)
Get PDFThe linear wave theory according to Airy/Laplace (1842) is widely used by engineers however violates the law of conservation of mass and considers local ground inclination α = 0⁰ only.Both shortcomings can be avoided(a) by extending Schulejkin\u27s mirror method to represent orbital kinematics over flat ground to inclinations 0⁰ ≤ α ≤ 90⁰ and(b) by referring to the phase shift Δϕ between incident and reflected waves according to the author´s definition of the complex reflection coefficient CRC.This contribution includes Exponentially Reduced Reflection (ERR) for the first time as a wave theory applicable to complex boundary conditions, considering a priori an important cause of wave deformation over inclined seafloor.For instance, the change of the total orbital kinematics (orbital paths, velocities and accelerations) related to the water surface is shown for decreasing water depths on a slope 1 : n = 1 : 2.In contrast to the Airy/Laplace theory, lower orbital velocities are obtained above the still water level, which is important with respect to the design of offshore structures
Exponentially Reduced Reflection (ERR) versusLinear Wave Theory (Airy/Laplace)
No full textThe linear wave theory according to Airy/Laplace (1842) is widely used by engineers however violates the law of conservation of mass and considers local ground inclination α = 0⁰ only.
Both shortcomings can be avoided
(a) by extending Schulejkin's mirror method to represent orbital kinematics over flat ground to inclinations 0⁰ ≤ α ≤ 90⁰ and
(b) by referring to the phase shift Δϕ between incident and reflected waves according to the author´s definition of the complex reflection coefficient CRC.
This contribution includes Exponentially Reduced Reflection (ERR) for the first time as a wave theory applicable to complex boundary conditions, considering a priori an important cause of wave deformation over inclined seafloor.
For instance, the change of the total orbital kinematics (orbital paths, velocities and accelerations) related to the water surface is shown for decreasing water depths on a slope 1 : n = 1 : 2.
In contrast to the Airy/Laplace theory, lower orbital velocities are obtained above the still water level, which is important with respect to the design of offshore structures
Computational Investigation on Tyrosine to Alanine Mutations Delaying the Early Stage of α-Synuclein Aggregation
No full textInvestigation on the Molecular Interactions Stabilizing the Structure of α-synuclein Fibril: An In silico Study
No full textReclaiming the past: Oral history and the legacy of integration in West Mount Airy, Philadelphia
No full textIn 1992, West Mount Airy Neighbors (WMAN), a Philadelphia community organization, embarked on an oral history project designed to capture the history of local efforts, beginning in the 1950s, to create and foster racial integration in the neighborhood. The project was designed to build a consciousness about the region\u27s past among current residents, in order to bring homeowners together and heighten community cohesion at a time when various social and economic forces threatened neighborhood viability. But even as WMAN saw the project as an opportunity to effect contemporary grassroots change, the group used the emerging narrative to reinforce an official version of the neighborhood\u27s historical efforts toward integration. Through the oral history project, WMAN developed a sanctioned and sanitized memory of the community, one that positioned the longtime organization to assert control over the scope of change going forward. © 2014 The Author
The tacnode kernel: equality of Riemann-Hilbert and Airy resolvent formulas
No full textWe study nonintersecting Brownian motions with two prescribed starting and ending positions, in the neighborhood of a tacnode in the time–space plane. Several expressions have been obtained for the critical correlation kernel that describes the microscopic behavior of the Brownian motions near the tacnode. One approach, due to
Kuijlaars, Zhang, and the author, expresses the kernel
via a 4 × 4 matrix-valued Riemann–Hilbert problem (RH problem). Another approach, due to Adler, Ferrari, Johansson, van Moerbeke, and Veto,
expresses the kernel via resolvents and Fredholm determinants of the Airy integral operator. In this paper, we prove the equivalence of both approaches. We also obtain a rank-2 property for the derivative of the tacnode kernel. Finally, we find an RH expression for the multitime extended tacnode kernel.sponsorship: Fund for Scientific Research Flandersstatus: Publishe
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