Search results for "EXPANSION"
showing 10 items of 630 documents
Application of the star-product method to the angular momentum quantization
1992
We define a *-product on ℝ3 and solve the polarization equation f*C=0 where C is the Casimir of the coadjoint representation of SO(3). We compute the action of SO(3) on the space of solutions. We then examine the case of non-zero eigenvalues of C, in order to find finite-dimensional representations of SO(3). Finally, we compute \(\sqrt C *\sqrt C \) as an asymptotic series of C. This gives an explanation of the use of the star square root of C in a paper by Bayen et al. instead of its natural square root.
On the use of fractional calculus for the probabilistic characterization of random variables
2009
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
High-pressure study of substrate material ScAlMgO4
2011
We report on the structural properties of ScAlMgO4 studied under quasi-hydrostatic pressure using synchrotron high-pressure x-ray diffraction up to 40 GPa. We also report on single-crystal studies of ScAlMgO4 performed at 300 K and 100 K. We found that the low-pressure phase remains stable up to 24 GPa. At 28 GPa, we detected a reversible phase transformation. The high-pressure phase is assigned to a monoclinic distortion of the low-pressure phase. No additional phase transition is observed up to 40 GPa. In addition, the equation of state, compressibility tensor, and thermal expansion coefficients of ScAlMgO4 are determined. The bulk modulus of ScAlMgO4 is found to be 143(8) GPa, with a str…
Microstructure–property relation and machine learning prediction of hole expansion capacity of high-strength steels
2021
Abstract The relationship between microstructure features and mechanical properties plays an important role in the design of materials and improvement of properties. Hole expansion capacity plays a fundamental role in defining the formability of metal sheets. Due to the complexity of the experimental procedure of testing hole expansion capacity, where many influencing factors contribute to the resulting values, the relationship between microstructure features and hole expansion capacity and the complexity of this relation is not yet fully understood. In the present study, an experimental dataset containing the phase constituents of 55 microstructures as well as corresponding properties, su…
Relations between compression and thermal contraction in 1,2,4-trichlorobenzene and melting of trichlorobenzene isomers
2015
The compression and thermal expansion of crystalline 1,2,4-trichlorobenzene, C6H3Cl3, 124TCB, investigated under isobaric and isothermal conditions, are in reverse relation, as for most of crystals, however, the isochoric strain along direction c is clearly different from those along a and b. Single crystals of 124TCB have been in situ grown under isochoric and isobaric conditions, at 270 K/0.1 MPa and 295 K/0.16 GPa, and also at 100 K/0.1 MPa and 295 K/0.64 GPa, when the unit-cell volume is similar. All crystallizations yielded the same phase, of monoclinic space group P21/n, with two symmetry-independent molecules (Z′ = 2). The structure is governed by Cl⋯Cl and Cl⋯H interactions and the …
Negative thermal expansion of quartz glass at low temperatures: An ab initio simulation study
2017
Abstract Using a mixed classical Molecular dynamics (MD)/ab initio simulation scheme combined with a quasi-harmonic approximation, we calculate the linear thermal expansion coefficient αL(T) in vitreous silica glasses. The systems are first cooled down by classical MD simulations. Then they are structurally relaxed by ab initio DFT calculations. The vibrational properties are calculated employing the frozen phonon method, and these results are finally used to calculate the Helmholtz free energy as a function of volume. In agreement with experiments, our simulations predict that αL(T) is negative at low temperatures up to T ≈ 150 K. In this low-temperature regime, the simulation results are …
ChPT parameters from tau-decay data
2015
Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Expansion.
Excimer laser technology in percutaneous coronary interventions: Cardiovascular laser society's position paper
2022
Excimer Laser Coronary Atherectomy (ELCA) is a well-established therapy that emerged for the treatment of peripheral vascular atherosclerosis in the late 1980s, at a time when catheters and materials were rudimentary and associated with the most serious complications. Refinements in catheter technology and the introduction of improved laser techniques have led to their effective use for the treatment of a wide spectrum of complex coronary lesions, such as thrombotic lesions, severe calcific lesions, non-crossable or non-expandable lesions, chronic occlusions, and stent under-expansion. The gradual introduction of high-energy strategies combined with the contrast infusion technique has enabl…
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .