Search results for "PROB"

Variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models

2016

Abstract The principle of minimum total potential energy and the primary principle of virtual power for stress gradient elasticity are presented as kinematic type constructs dual of analogous static type principles from the literature (Polizzotto, 2014; Polizzotto, 2015a). The extra gradient-induced boundary conditions are formulated as “boundary congruence conditions” on the microstructure’s deformation relative to the continuum, which ultimately require that the normal derivative of the stresses must vanish at the boundary surface. Two forms of the governing PDEs for the relevant boundary-value problem are presented and their computational aspects are discussed. The Timoshenko beam and th…

A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams

2013

Abstract A new one-dimensional model for the dynamic problem of magneto-electro-elastic generally laminated beams is presented. The electric and magnetic fields are assumed to be quasi-static and a first-order shear beam theory is used. The electro-magnetic problem is first solved in terms of the mechanical variables, then the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, which involve the third spatial derivative of the transverse displacement, also occur as a result of the …

A mechanically based approach to non-local beam theories

2011

A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…

Analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

2009

Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the def…

Aika-, ikä- ja kohorttivaikutukset kotitalouksien rahoitusvarallisuuden rakenteisiin Suomessa vuosina 1994-2004

2007

Lévy flights in confining potentials.

2009

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are considered: those driven by Langevin equation with L\'{e}vy noise and those, named by us topological L\'{e}vy processes (occurring in systems with topological complexity like folded polymers or complex networks and generically in inhomogeneous media), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary (eventually asymptotic) probability densit…

Improved Switching Strategy for Selective Harmonic Elimination in DC-AC Signal Generation via Pulse-Width Modulation

2013

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/870904 Open Access We present an advanced design methodology for pulse-width-modulated (PWM) DC-AC signal generation. Using design methods based on the Walsh transform, AC sinusoidal signals can be approximated by suitable PWM signals. For different AC amplitudes, the switching instants of the PWM signals can be efficiently computed by using appropriate systems of explicit linear equations. However, the equation systems provided by conventional implementations of this approach are typically only valid for a restricted interval of AC amplitudes a…

Photon Scanning Tunneling Microscopy and Reflection Scanning Microscopy

1991

The Photon Scanning Tunneling Microscope (PSTM) is the photon analogue to the Electron Scanning Tunneling Microscope (ESTM). It uses the evanescent field due to the total internal reflection (TIR) of a light beam in a prism modulated by a sample attached to the prism. The exponential decay of the evanescent field is characterized by the penetration depth dp and depends on the angle of incidence θ, the wavelength and polarization of the incident beam. Changes in intensity are monitored by a probe tip scanned over the surface, and the data are processed to generate an image of the sample. Images produced by a prototype instrument are shown to have a vertical resolution of about 3 A and a late…

Resolution of the photon scanning tunneling microscope: influence of physical parameters

1992

Abstract The photon scanning tunneling microscope (PSTM) is the photon analogue of the electron scanning tunneling microscope (ESTM). It uses the evanescent field due to total internal reflection (TIR) of a light beam in a prism modulated by a sample placed on the base of the prism. Our experimental results shown details which present a lateral size as small as 200 A. The PSTM axial resolution is more difficult to evaluate. It is a function of the roughness of the sample. For very smooth samples, images shown an axial resolution of about 10 A. At last we discuss how both lateral and axial resolution can be affected by several parameters such as the tip surface distance and the roughness of …

Fazioni e popolo in una provincia del dominio pontificio fra XIII e XIV secolo

2021

Between the 13th and 14th centuries, a number of cities in the inchoative papal state experimented a system of self-government that allowed the Guelph and Ghibelline factions, formally represented in those same bodies on an equal footing, to work alongside the more strictly communal magistracies. The case of Todi is rather well known, given the role that Bartolo da Sassoferrato assigns to it in his Tractatus de guelphis et gebellinis (ca. 1350), but current research has already ascertained that this political tradition appeared at least around 1260. Some evidence can suggest, however, that some form of integration of factions into the local institutional framework was possible elsewhere, an…