Search results for "linear"
showing 10 items of 7165 documents
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
Comparative Theoretical Analysis of BN Nanotubes Doped with Al, P, Ga, As, In, and Sb
2013
SUMMARY AND CONCLUDING REMARKS We have performed large-scale first-principles calculations ofthe electronic structure of (5,5) boron nitride nanotubescontaining the following substitutional impurity atoms: Al, P,Ga, As, In, and Sb. Calculations have been performed using thetwo methods: (i) linear combination of atomic orbitals(LCAO) with the atomic-centered Gaussian-type functions asa basis set and (ii) linearized augmented cylindrical wave(LACW) accompanied with the local density functional andmuffin-tin approximations for the electronic potential. In arelatively good qualitative agreement, both methods predict lowformation energies and, thus, relative stability of point defectsthat are assoc…
Strategies for numerical simulation of linear friction welding of metals: a review
2017
Linear friction welding (LFW) is a solid-state joining process used to weld non-axisymmetric components. Material joining is obtained through the reciprocating motion of two specimens undergoing an axial force. During this process, the heat source is determined by the frictional work transformed into heat. This results in a local softening of the material and plays a key role in the onset of the bonding conditions. In this paper, a critical analysis of the different approaches used to simulate the LFW processes is provided. The focus of the paper is the comparison of different modeling strategies and the most relevant outputs available, i.e. temperature, strain and stress distribution, mate…
The helicoidal magnetic generator
2016
Recently helicoidal generator for the exploitation of sea wave energy has been proposed. This device can convert both the vertical and rotational movement of seawaves. The electrical energy generated by such a device must be converted and conditioned in order to match the instantaneous utility requirements and a power link from the sea to an interconnection is needed. In this paper, the authors propose a mathematical model of this device and preliminarily present a prototype of the machine.
ABSOLUTE THERMOELECTRIC POWER OF Pb–Sn ALLOYS
2011
International audience; In this work, absolute thermoelectric power (ATP) of Pb, Sn, Pb-20 wt.% Sn, Pb-40 wt.% Sn, Pb-60 wt.% Sn, Pb-80 wt.% Sn are measured. Measurements are performed in a temperature gradient furnace from 20 degrees C to 500 degrees C, for both solid and liquid states. Temperatures are measured with T-type copper-constantan thermocouples, while voltage signal between copper electrodes of those thermocouples is recorded in order to calculate ATP of the sample metal.
A multilayer model for self-propagating high-temperature synthesis of inter-metallic compounds
2007
International audience; Self-propagating high-temperature synthesis of intermetallic compounds is of wide interest. We consider reactions in a binary system in which the rise and fall of the temperature during the reaction is such that one of the reacting metals melts but not the other. For such a system, using the phase diagram of the binary system, we present a general theory that describes the reaction taking place in a single solid particle of one component surrounded by the melt of the second component. The theory gives us a set of kinetic equations that describe the propagation of the phase interfaces in the solid particle and the change in composition of the melt that surrounds it. I…
Isothermal relaxation of discommensurations in K2ZnCl4
1994
At the incommensurate-ferroelectric transition temperature T c of K 2 ZnCl 4 , the dielectric susceptibility contains an anomalous contribution both above and below T c . Previous quasi-static dielectric measurements and hysteresis loops demonstrated that this anomalous part arises from the peculiar dynamics of discommensurations. We have used isothermal dielectric measurements to get some insight into the long time dynamics of these discommensurations. We have found that the characteristic relaxation times τ are of the order of 10 4 s in the incommensurate and in the ferroelectric phase. Even more unusual is a non-monotonous relaxation which is observed in a restricted temperature range ab…
Analysis of nonlinear time-dependent properties of carbon fiber reinforced plastic under off-axis loading
2021
Abstract Polymeric composites are rheonomic materials and their deformation can be described using the hereditary elasticity relations which allow for describing the mechanical behavior under time-variable loading with consideration of the influence of temperature and other operational factors. A system of hereditary-type constitutive relations is proposed for off-axis specimens of a unidirectional carbon fiber-reinforced plastic subjected to loading at different strain rates. Using the algebra of resolvent operators and inverted transformation, the constitutive equations allowing of description of anisotropy of rheological properties and, in particular, sensitivity to strain rates are deri…
Magneto-optical properties of two-layer film systems based on Fe and Cr
2020
The results of the investigation of two-layer Fe/Cr systems using the magneto-optical Kerr effect (MOKE) are presented in this paper. The samples were obtained by thermal evaporation in a vacuum with a thickness of individual layers from 2 nm to 50 nm. It was found that the presence of the Cr layer significantly affects the values of the coercivity and the Kerr angle. At a substrate temperature of 450 K, the value of the coercivity is almost half that of the same sample obtained at room temperature of the substrate. In addition, the influence of the order of deposition of layers, as well as the effect of a thin gold protective layer on the parameters measured by the Kerr method, is shown. …