Search results for " Classical Physic"
showing 10 items of 31 documents
Thermodynamics of Substances with Negative Thermal Expansion Coefficient
2000
The 1st law of thermodynamics for heat exchange is dQ=dU+PdV. According to K. Martinas etc., J. Non-Equil. Thermod. 23 (4), 351-375 (1988), for substances with negative thermal expansion coefficient, P in this law is negative. In the present paper it has been shown that P for such substances is positive but the sign before P must be minus not plus: dQ=dU-PdV.
General invertible transformation and physical degrees of freedom
2017
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of …
Pre-Stressed Sub-Surface Contribution on Bulk Diffusion in Metallic Solids
2011
Our recent modelling works and corresponding numerical simulations realized to describe the UO2 oxidation processes confirm the theory showing that an applied mechanical strain can strongly affect the local oxygen diffusion in a stressed solid. This result allows us to assume that stress field, previously applied at the surface of a metallic sample on several microns, will delay the degradation during its oxidation. Considering this hypothesis, we implemented a FEM simulation code developed in our laboratory to numerically investigate some different stress fields applied on a sample sub-surface, that might significantly modify the volume diffusion of oxygen during the oxidation process. The…
A neutron tomography study: Probing the spontaneous crystallization of randomly packed granular assemblies
2018
We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction around 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The ext…
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
2014
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…
Mechanical Properties of Pore-Spanning Lipid Bilayers Probed by Atomic Force Microscopy
2006
AbstractWe measure the elastic response of a free-standing lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar gold-coated alumina substrate with a chemisorbed 3-mercaptopropionic acid monolayer displaying circular pores of very well defined and tunable size, over which bilayers composed of N,N,-dimethyl-N,N,-dioctadecylammonium bromide or 1,2-dioleoyl-3-trimethylammonium-propane chloride were spread. Centrally indenting these “nanodrums” with an atomic force microscope tip yields force-indentation curves, which we quantitatively analyze by solving the corresponding shape equations of continuum curvature elasticity. Since the measured respon…
Transverse shear warping functions for anisotropic multilayered plates
2012
In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the warping functions and their derivatives. The variational calculus leads to a differential system of equations which warping functions must verify. Solving this system requires the choice of values for the (global) shear strains and their derivatives. A particular choice, which is justified for cross-ply laminates, leads to excellent results. For single layer isotropic and orthotropic plates, an analytical expression of the warping functions is given. They invol…
The generalized plane piezoelectric problem: Theoretical formulation and application to heterostructure nanowires
2016
We present a systematic methodology for the reformulation of a broad class of three-dimensional (3D) piezoelectric problems into a two-dimensional (2D) mathematical form. The sole underlying hypothesis is that the system geometry and material properties as well as the applied loads (forces and charges) and boundary conditions are translationally invariant along some direction. This class of problems is commonly denoted here as the generalized plane piezoelectric (GPP) problem. The first advantage of the generalized plane problems is that they are more manageable from both analytical and computational points of view. Moreover, they are flexible enough to accommodate any geometric cross secti…
An educational path for the magnetic vector potential and its physical implications
2013
We present an educational path for the magnetic vector potential A aimed at undergraduate students and pre-service physics teachers. Starting from the generalized Ampere–Laplace law, in the framework of a slowly varying time-dependent field approximation, the magnetic vector potential is written in terms of its empirical references, i.e. the conduction currents. Therefore, once the currents are known, our approach allows for a clear and univocal physical determination of A, overcoming the mathematical indeterminacy due to the gauge transformations. We have no need to fix a gauge, since for slowly varying time-dependent electric and magnetic fields, the ‘natural’ gauge for A is the Coulomb o…
Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops
2005
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by …