Search results for " solution"
showing 10 items of 3084 documents
Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution
2008
An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.
Tuning the magnetic properties in the layered molecular based magnets A[FeIIRuxIIIM1−xIII(ox)3] (MIII=Cr or Fe; ox=oxalate; A=organic or organometall…
2001
Abstract The magnetic properties of the family of layered molecular magnets A[FeIIMIII(ox)3] (MIII=Cr, Fe, Ru; ox=oxalate; A+=[NBu4]+, [ CoCp 2 ∗ ] + ) are reported. In particular, a detailed magnetic study of the solid solutions FeII(RuIIICrIII) and FeII(RuIIIFeIII) has been undertaken. We show that in these magnets both, transition temperatures and coercive fields, can be easily tuned by changing the chemical composition of the material, i.e. the ratio RuIII/MIII (MIII=Cr, Fe) within the magnetic layers and the type of cation A+ inserted in between the layers. Coercive fields as high as 2.2 T have been reached in this way.
Symmetric boundary element method versus finite element method
2002
The paper examines the effectiveness of the symmetric boundary element formulation when the continuum body is subdivided into large elements called macro-elements. The approach proposed combines a strong reduction of variables with an elastic solution close to the real response. Indeed, if the displacement method is used, this approach permits one to determine for every macro-element a relationship connecting the weighted traction vector defined on the sides of the interface boundary with the node displacement vector of the same boundary and with the external action vector. Such a strategy is very similar to that followed through the finite element method, but with the advantages of having …
Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals
2012
Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.
Path integral solution handled by Fast Gauss Transform
2009
Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…
Bending stress fields in composite laminate beams by a boundary integral formulation
1999
Abstract The elasticity of a composite laminate under bending loads is approached through a boundary integral formulation and solved by the boundary element method. The integral equations governing the behaviour of each layer within the laminate, are deduced using the reciprocity theorem. Exact analytical singular solutions of the generalized orthotropic elasticity, i.e. the fundamental solutions of the problem, are employed as the kernels of the integral equation. The formulation does not make any assumption as to the nature of the elastic response and it allows consideration of general section geometries and stacking sequences. The solution is obtained through the enforcement of the inter…
Path Integral Method for Nonlinear Systems Under Levy White Noise
2017
In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under…
Freeze-dried precursor-based synthesis of new polymetallic oxynitrides, V1−u−zCruMoz(OxNy),V1−u−zCruWz(OxNy), Cr1−u−zMouWz(OxNy) (u, z=0.2, 0.33, 0.4…
2005
Abstract Interstitial polymetallic oxynitrides in the solid solution series V 1− u − z Cr u Mo z (O x N y ), V 1− u − z Cr u W z (O x N y ) and Cr 1− u − z Mo u W z (O x N y ) ( u , z = 0.2, 0.33, 0.4, 0.6, u + z z Cr z Mo z W z (O x N y ) ( z = 0.25) composition, can be obtained by ammonolysis of precursors resulting from the freeze-drying of aqueous solutions of the simple metal salts NH 4 VO 3 , (NH 4 ) 2 CrO 4 , (NH 4 ) 6 Mo 7 O 24 ·4H 2 O and (NH 4 ) 6 W 12 O 39 ·18H 2 O. A study of the influence of the preparative variables on the outcomes of this procedure is presented. Compounds in the V 1− u − z Cr u Mo z (O x N y ) series have been prepared as single phases by direct ammonolys…
Dynamic response of beams excited by moving oscillators: Approximate analytical solutions for general boundary conditions
2023
In this paper, the dynamic response of an Euler-Bernoulli beam with general boundary conditions (BCs) and subject to a moving oscillator is examined. Notably, novel approximate closed-form expressions are determined for the vertical responses of both the beam and the moving oscillator, specifically considering the effect of damping in these systems, commonly omitted in standard approaches in the literature. In this regard, a modal superposition procedure is adopted and combined with an appropriate expansion-based approach of the dynamic response of the system, which naturally arises considering the oscillator-beam mass ratio to be reasonably small. Further, general boundary conditions are t…
Direct stiffness matrices of BEs in the Galerkin BEM formulation
2001
Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.