scholarly journals Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210167
Author(s):  
Tomasz M. Tyranowski
Keyword(s):  
Maxwell Equations ◽  
Variational Principles ◽  
Particle Method ◽  
Variational Characterization ◽  
Particle In Cell ◽  
Poisson Equations ◽  
Stochastic Variational Principles ◽  
Further Development ◽  
Stochastic Particle

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.

scholarly journals Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nicolas Crouseilles ◽  
Paul-Antoine Hervieux ◽  
Yingzhe Li ◽  
Giovanni Manfredi ◽  
Yajuan Sun
Keyword(s):  
Phase Space ◽  
Maxwell Equations ◽  
Stimulated Raman Scattering ◽  
Extended Phase ◽  
Five Dimensions ◽  
Particle In Cell ◽  
Spin Effects ◽  
Dimensional Phase Space ◽  
Spin Polarized ◽  
Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

Characterization of Biosensor Detection Process at Ultra-Low Concentration Through a Stochastic Particle Model

2010 ◽  
Author(s):  
Samar Shah ◽  
Yaling Liu ◽  
Walter Hu
Keyword(s):  
Liquid Solution ◽  
Particle Model ◽  
Low Concentration ◽  
Detection Process ◽  
Nanoparticle Detection ◽  
Early Disease Detection ◽  
Cost Efficient ◽  
New Applications ◽  
Stochastic Particle

Biosensor detection process involves binding between biomolecules in a solution and a functionalized sensor surface. These sensors are time and cost efficient, sensitive, and enable new applications in medicine, drug design, and environmental monitoring. In literatures, various biosensor designs have been proposed, such as planar electrodes, nanowire, and nanospheres for different applications. However, to fully realize the potentials of these biosensors for biomarker/nanoparticle detection, several challenges must be addressed. In particular, ultra-sensitive biosensors are needed for detection of ultra-low concentration biomarkers such as cancer markers for early disease detection. The goal of this paper is to understand the diffusion process of biomarkers in a liquid solution and the binding with nanosensor surface through a stochastic particle model.

scholarly journals Application of Dynamic and Static Light Scattering for Size and Shape Characterization of Small Extracellular Nanoparticles in Plasma and Ascites of Ovarian Cancer Patients

2021 ◽  
Vol 22 (23) ◽  
pp. 12946
Author(s):  
Ksenija Kogej ◽  
Darja Božič ◽  
Borut Kobal ◽  
Maruša Herzog ◽  
Katarina Černe
Keyword(s):  
Ovarian Cancer ◽  
Light Scattering ◽  
Spherical Particles ◽  
Radius Of Gyration ◽  
Non Invasive ◽  
Peritoneal Washing ◽  
Angular Dependency ◽  
Shape Characterization ◽  
Further Development

In parallel to medical treatment of ovarian cancer, methods for the early detection of cancer tumors are being sought. In this contribution, the use of non-invasive static (SLS) and dynamic light scattering (DLS) for the characterization of extracellular nanoparticles (ENPs) in body fluids of advanced serous ovarian cancer (OC) and benign gynecological pathology (BP) patients is demonstrated and critically evaluated. Samples of plasma and ascites (OC patients) or plasma, peritoneal fluid, and peritoneal washing (BP patients) were analyzed. The hydrodynamic radius (Rh) and the radius of gyration (Rg) of ENPs were calculated from the angular dependency of LS intensity for two ENP subpopulations. Rh and Rg of the predominant ENP population of OC patients were in the range 20–30 nm (diameter 40–60 nm). In thawed samples, larger particles (Rh mostly above 100 nm) were detected as well. The shape parameter ρ of both particle populations was around 1, which is typical for spherical particles with mass concentrated on the rim, as in vesicles. The Rh and Rg of ENPs in BP patients were larger than in OC patients, with ρ ≈ 1.1–2, implying a more elongated/distorted shape. These results show that SLS and DLS are promising methods for the analysis of morphological features of ENPs and have the potential to discriminate between OC and BP patients. However, further development of the methodology is required.

scholarly journals Characterization of the Common japonica-Originated Genomic Regions in the High Yielding Varieties Developed from Inter-Subspecific Crosses in Rice (Oryza sativa L.)

2020 ◽  
Author(s):  
Jeonghwan Seo ◽  
So-Myeong Lee ◽  
Jae-Hyuk Han ◽  
Na-Hyun Shin ◽  
Yoon Kyung Lee ◽  
...  
Keyword(s):  
Molecular Breeding ◽  
Snp Markers ◽  
Yield Potential ◽  
Breeding Programs ◽  
Wx Gene ◽  
High Yielding Varieties ◽  
Indica And Japonica Subspecies ◽  
Genomic Regions ◽  
Further Development

The inter-subspecific crossing between indica and japonica subspecies in rice have been utilized to improve yield potential in temperate rice. In this study, a comparative study of the genomic regions in the eight high yielding varieties (HYVs) was conducted with those of the four non-HYV varieties. NGS mapping on the Nipponbare reference genome identified a total of 14 common genomic regions of japonica-originated alleles. Interestingly, the HYVs shared the japonica-originated genomic regions on the nine chromosomes, although they were developed from different breeding programs. A panel of 94 varieties was classified into four varietal groups with the 39 SNP markers from 39 genes residing the japonica-originated genomic regions and 16 additional trait-specific SNPs. As expected, the japonica originated genomic regions were present only in JAP and HYV groups with exceptions for Chr4-1 and Chr4-2. The Wx gene located within Chr6-1 was present in HYV and JAP variety groups, while the yield-related genes were conserved as indica alleles in HYVs. The japonica-originated genomic regions and alleles shared by HYVs can be employed in molecular breeding programs for further development of HYVs in rice.

Sign in / Sign up

Export Citation Format

Share Document