scholarly journals Applying splitting methods with complex coefficients to the numerical integration of unitary problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sergio Blanes ◽  
Fernando Casas ◽  
Alejandro Escorihuela-Tomàs
Keyword(s):  
Numerical Integration ◽  
Numerical Approximation ◽  
Splitting Methods ◽  
Time Dependent ◽  
Small Step ◽  
Time Intervals ◽  
Long Time ◽  
Complex Coefficients ◽  
Pseudo Spectral ◽  
Spectral Discretization

<p style='text-indent:20px;'>We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schrödinger equation. We prove that a particular class of integrators are conjugate to unitary methods for sufficiently small step sizes when applied to problems defined in the group <inline-formula><tex-math id="M1">\begin{document}$ \mathrm{SU}(2) $\end{document}</tex-math></inline-formula>. In the general case, the error in both the energy and the norm of the numerical approximation provided by these methods does not possess a secular component over long time intervals, when combined with pseudo-spectral discretization techniques in space.</p>

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

An Accelerated Retarded Potential Method for Time Dependent Acoustic Wave Scattering

1995 ◽  
Author(s):  
Toufic S. Abboud ◽  
Joseph M. Gharib ◽  
Jean Claude Nédélec ◽  
Toni G. Sayah
Keyword(s):  
Finite Element Method ◽  
Integral Equation ◽  
Wave Scattering ◽  
Numerical Approximation ◽  
Mesh Size ◽  
Integral Equation Method ◽  
Potential Method ◽  
Boundary Integral ◽  
Time Dependent ◽  
Acoustic Wave Scattering

Abstract We are interested in the numerical approximation of the problem of the scattering of a transient acoustic plane wave by a bounded obstacle in IR2 or IR3, using the boundary integral equation method. In the frequency domain it has been recently developed a boundary finite element method where the mesh size is like O(λ1/3) instead of O(λ) (λ is the wavelength) and where the obstacle is convex. This paper presents the implementation of the idea on the retarted potential representation.

Super-Fine Structure in the Critical Flow-Rate of Critical Flow Venturi Nozzles

2002 ◽  
Author(s):  
Masahiro Ishibashi
Keyword(s):  
Fine Structure ◽  
Steady State ◽  
Discharge Coefficient ◽  
Constant Pressure ◽  
Pressure Ratio ◽  
Critical Flow ◽  
Time Intervals ◽  
Critical Flow Rate ◽  
A Value ◽  
Long Time

It is shown that critical flow Venturi nozzles need time intervals, i.e., more than five hours, to achieve steady state conditions. During these intervals, the discharge coefficient varies gradually to reach a value inherent to the pressure ratio applied. When a nozzle is suddenly put in the critical condition, its discharge coefficient is trapped at a certain value then afterwards approaches gradually to the inherent value. Primary calibrations are considered to have measured the trapped discharge coefficient, whereas nozzles in applications, where a constant pressure ratio is applied for a long time, have a discharge coefficient inherent to the pressure ratio; inherent and trapped coefficients can differ by 0.03–0.04%.

scholarly journals Evaluation of spermicidal activity of saponosides from Saponaria officinalis / Caryophyllaceae, Glycyrrhizia glabra / Fabaceae and Herniaria glabra / Caryophyllaceae

2021 ◽  
Author(s):  
Mohamed Réda Sefrioui ◽  
Ibrahim Sbai El Othmani ◽  
Halima Filali ◽  
Sanae Derfoufi ◽  
Soufiane Derraji ◽  
...  
Keyword(s):  
Natural Products ◽  
Side Effects ◽  
Time Dependent ◽  
Time Intervals ◽  
Dependent Effect ◽  
Time Dependent Effect ◽  
Sperm Mobility ◽  
In Vitro Effects ◽  
Saponaria Officinalis

Background and objective. Chemical spermicides currently marketed and widely used are known to have many side effects. Thereby, and in order to look for more tolerated natural spermicidal agents, the aim of this work was to evaluate the spermicidal potential of saponin extracts from the roots of Saponaria officinalis / Caryophyllaceae, Glycyrrhizia glabra / Fabaceae, and Herniaria glabra / Caryophyllaceae by studying their in vitro effects on sperm mobility and vitality. Methods. Methanolic saponin extracts from the plants roots were performed. Sperm suspensions were prepared by centrifugation on a PureSperm® density gradient (70 and 45%) and incubated with various concentrations of saponin extracts (50, 250, 500 and 750 mg/mL) at 37°C. The spermicidal activity was evaluated by studying the mobility and vitality of spermatozoa at different time intervals ranging from 10 to 240 minutes. Results. A dose and time dependent effect on sperm mobility and vitality was observed for our extracts. Extracts from Saponaria officinalis roots induced an irreversible immobilization and a total non-viability of sperm within 10 minutes at a concentration of 750 mg/mL. A similar effect was observed within 30 minutes at 750 mg/mL for Herniaria glabra extract and within 90 minutes at 500 mg/ml for Glycyrrhizia glabra extract. Conclusion. The results of our study showed that the saponin extracts of our plants roots possess potent in vitro dose and time dependant spermicidal effect. These natural products could therefore represent a safer and better tolerated alternative to chemical spermicides.

scholarly journals ANALYSIS OF THE TIME‐DEPENDENT BEHAVIOUR OF COMPOSITE CROSS‐SECTIONS BY LAPLACE‐TRANSFORM

2005 ◽  
Vol 11 (3) ◽  
pp. 203-209
Author(s):  
Erich Raue ◽  
Thorsten Heidolf
Keyword(s):  
Laplace Transform ◽  
Cross Sections ◽  
Composite Structures ◽  
Time Dependent ◽  
Time Interval ◽  
Final State ◽  
Long Time ◽  
Time Dependent Behaviour ◽  
Linear Differential ◽  
Dependent Behaviour

Composite structures consisting of precast and cast in‐situ concrete elements are increasingly common. These combinations demand a mechanical model which takes into account the time‐dependent behaviour and analysis of the different ages of the connected concrete components. The effect of creep and shrinkage of the different concrete components can be of relevance for the state of serviceability, as well as for the final state. The long‐time behaviour of concrete can be described by the rate‐of‐creep method, combined with a discretisation of time. The internal forces are described for each time interval using a system of linear differential equations, which can be solved by Laplace‐transform.

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