Search results for "Calculus"

Dynamic path length changes in all-fiber mirrors: Transmission modulation

1995

Abstract In this paper, we present a technique to modulate the transmission of an all-fiber mirror. This technique is based on the phase modulation of the light in the fiber loop, combined with the time delay between the clockwise and anticlockwise propagating beams. Using Jones calculus, a theoretical analysis has been carried out to describe the effects of static polarization changes and a dynamic phase modulation. An experimental all-fiber optical mirror has been constructed, and using a 1–MHz piezoelectric disc as the phase modulator, we demonstrate that it is possible to achieve either a 1–MHz or 2–MHz transmission modulation by adjusting the polarization state.

Synchronization of Two Photoelastic Light Modulators to Obtain Müeller Matrix

2013

We report a method for the temporal synchronization of two photoelastic light modulators. For synchronizing, we used the transistor-transistor logic output signals from each modulator, which contain the information on the light polarization. These signals were introduced in a phase-detector circuit, which provided the phase difference value between both modulators. Three optical devices were used to test the synchronization method proposed: a polarizer, a half-wave, and a quarter-wave retarder plate. The value of each of the elements of the Mueller matrix for these devices was obtained using the method of the 36 measurements. The results show a high correlation between the theoretical and e…

Variation of Area Variables in Regge Calculus

1998

We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and appropriate constraints are imposed between the variations, the Einstein-Regge equations are recovered.

Differential calculus on 'non-standard' (h-deformed) Minkowski spaces

1997

ELASTIC WAVES: MENTAL MODELS AND TEACHING/LEARNING SEQUENCES

2006

In last years many research studies have pointed out relevant student difficulties in understanding the physics of mechanical waves. Moreover, it has been reported that these difficulties deal with some fundamental concepts as the role of the medium in wave propagation, the superposition principle and the mathematical description of waves involving the use of functions of two variables. In the context of pre-service courses for teacher preparation a teaching/learning (T/L) sequence based on using simple RTL experiments and interactive simulation environments aimed to show the effect of medium properties on the propagation speed of a wave pulse, has been experimented. Here, preliminary resul…

Constraints on Area Variables in Regge Calculus

2000

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.

Stochastic Kinetics with Wave Nature

2003

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

The influence of topological phase transition on the superfluid density of overdoped copper oxides

2017

We show that a topological quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bo\^zovi\'c, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. We demonstrate that 1) at temperature $T=0$, the superfluid density $n_s$ turns out to be considerably smaller than the total electron density; 2) the critical temperature $T_c$ is controlled by $n_s$ rather than by doping, and is a linear function of the $n_s$…

Innovative modeling of Tuned Liquid Column Damper motion

2015

Abstract In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Sin…

Fractional visco-elastic systems under normal white noise

2011

In this paper an original method is presented to compute the stochastic response of singledegree- of-freedom structural systems with viscoelastic fractional damping. The key-idea stems from observing that, based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion can be reverted to a coupled linear system involving additional degrees of freedom, the number of which depends on the discretization adopted for the fractional derivative operator. The method applies for fractional damping of arbitrary order a (0 < α < 1). For most common input correlation functions, including a Gaussian white noise, …