1,721,012 research outputs found
Casimir Energies in a One-Dimensional Cavity with a Fluctuating Boundary
No full textWe consider a massless scalar field in a one-dimensional cavity with one fixed and one mobile wall. We assume that the mobile wall is also subjected to a harmonic potential, and its mechanical degrees of freedom are treated quantum-mechanically. The wall's position has
thus quantum fluctuations around the equilibrium position.
The possible motion of the wall makes the cavity length variable, and this gives rise to a wall-field interaction and an effective interaction between the modes of the cavity. We use an effective Hamiltonian, originally introduced by C. K. Law, to describe our system in terms of field modes
relative to the equilibrium position of the mobile wall. We obtain by perturbation theory the dressed ground state of the wall-field coupled system, which contains pairs of virtual quanta of the field and excitations of the wall's mechanical degrees of freedom.
We evaluate the average number of virtual excitations in each mode of the cavity, induced by the effective wall-field interaction, as well as the renormalized field energy density inside the cavity. We show that the quantum fluctuations of the wall's position significantly affect the field
energy density in the cavity, in particular in the proximity of the mobile wall. We also consider a statistical average of the energy density on the position of the fluctuating boundary, in order to discuss the known problem of the divergence of field energy densities at the boundaries. All these quantities are then compared with analogous quantities for a cavity with fixed walls. We find a correction to the Casimir potential energy and to the field energy density in the cavity,
due to the position fluctuations of the cavity wall, and discuss how these corrections depend on relevant parameters of the mobile wall, in particular its plasma frequency, mass and frequency of the harmonic potential. Observability of these new effects is also discussed, as well as the relation to the dynamical Casimir effect
Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
No full textWe consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casimir potential energy between the cavity walls. We also find a change of the field energy density in the cavity, particularly relevant in the proximity of the mobile wall, yielding a correction to the Casimir-Polder interaction with a polarizable body placed inside the cavity. Similarities and differences of our results with the dynamical Casimir effect are also discussed
Fractional differential equations solved by using Mellin transform
No full textIn this paper, the solution of the multi-order differential equations, by using Mellin transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands
Mellin transform approach for the solution of coupled systems of fractional differential equations
Get PDFIn this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized for
A physically based connection between fractional calculus and fractal geometry
Get PDFWe show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry. (C) 2014 Elsevier Inc. All rights reserved.</p
Fractional calculus for the solution of non-linear stochastic oscillators with viscous dampers devices
No full textFluid viscoelastic dampers are of great interest in different fields of engineering. Examples of their
applications can be found in seismic mitigation design of structures or in vibration absorption in
airplane suspension. Such devices introduce a non-linear dissipative term in the equation of motion
and therefore, the solution of even a single degree of freedom system excited by a white noise
process, becomes prohibitive. The solution is usually obtained by approximated methods, like the
stochastic linearization technique.
In this paper it is shown that, by means of fractional operators, it is possible to find the solution
of oscillators provided with fluid viscoelastic devices, approaching the problem in its originally nonlinear
form. Comparison with solutions obtained by Monte Carlo simulation are finally discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Field observables near a fluctuating boundary
Get PDFWe review several aspects related to the confinement of a massless scalar field in a cavity with a movable conducting wall of finite mass, free to move around its equilibrium position to which it is bound by a harmonic potential, and whose mechanical degrees of freedom are described quantum mechanically. This system, for small displacements of the movable wall from its equilibrium position, can be described by an e↵ective interaction Hamiltonian between the field and the mirror, quadratic in the field operators and linear in the mirror operators. In the interacting, i.e. dressed, ground state, we first consider local field observables such as the field energy density: we evaluate changes of the field energy density in the cavity with the movable wall with respect to the case of a fixed wall, and corrections to the usual Casimir forces between the two walls. We then investigate the case of two one-dimensional cavities separated by a movable wall of finite mass, with two massless scalar fields defined in the two cavities. We show that in this case correlations between the squared fields in the two cavities exist, mediated by the movable wall, at variance with the fixed-wall case
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