The role of pseudo-eigenvalues of the Boltzmann collision operator in thermalization problems

1983 ◽  
Vol 61 (7) ◽  
pp. 1038-1041 ◽  
Author(s):  
R. Blackmore ◽  
B. Shizgal
Keyword(s):  
Hard Sphere ◽  
Large Fraction ◽  
Collision Operator ◽  
Matrix Methods ◽  
Continuum Spectrum ◽  
Rigorous Treatment ◽  
Boltzmann Collision Operator ◽  
The Continuum

The calculation of the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigenvalues, a large fraction of which are unconverged and lie in the continuum spectrum of the operator. The role of these pseudo-eigenvalues is examined. The results strongly suggest that for practical calculations the rigorous treatment of the continuum is not necessary provided that a moderately large number of pseudo-eigenvalues are included.

scholarly journals Some Estimates on the Boltzmann Collision Operator

1997 ◽  
Vol 07 (07) ◽  
pp. 1023-1033 ◽  
Author(s):  
Jens Struckmeier
Keyword(s):  
Density Function ◽  
Interaction Potential ◽  
Hard Sphere ◽  
Collision Operator ◽  
Gain Term ◽  
Boltzmann Collision Operator ◽  
Maxwellian Molecules ◽  
Collision Kernels ◽  
Loss Term

The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L∞-norm of the gain term can be bounded in terms of the L1- and L∞-norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L∞-norm of the density function and the loss term of the Boltzmann collision operator.

scholarly journals The role of mergers and interactions in driving the evolution of dwarf galaxies over cosmic time

2020 ◽  
Vol 500 (4) ◽  
pp. 4937-4957 ◽  
Author(s):  
G Martin ◽  
R A Jackson ◽  
S Kaviraj ◽  
H Choi ◽  
J E G Devriendt ◽  
...  
Keyword(s):  
Star Formation ◽  
Dwarf Galaxies ◽  
Large Fraction ◽  
Structural Evolution ◽  
Cosmic Time ◽  
Stellar Mass ◽  
High Mass ◽  
Key Drivers ◽  
Mass Assembly

ABSTRACT Dwarf galaxies (M⋆ < 109 M⊙) are key drivers of mass assembly in high-mass galaxies, but relatively little is understood about the assembly of dwarf galaxies themselves. Using the NewHorizon cosmological simulation (∼40 pc spatial resolution), we investigate how mergers and fly-bys drive the mass assembly and structural evolution of around 1000 field and group dwarfs up to z = 0.5. We find that, while dwarf galaxies often exhibit disturbed morphologies (5 and 20 per cent are disturbed at z = 1 and z = 3 respectively), only a small proportion of the morphological disturbances seen in dwarf galaxies are driven by mergers at any redshift (for 109 M⊙, mergers drive under 20 per cent morphological disturbances). They are instead primarily the result of interactions that do not end in a merger (e.g. fly-bys). Given the large fraction of apparently morphologically disturbed dwarf galaxies which are not, in fact, merging, this finding is particularly important to future studies identifying dwarf mergers and post-mergers morphologically at intermediate and high redshifts. Dwarfs typically undergo one major and one minor merger between z = 5 and z = 0.5, accounting for 10 per cent of their total stellar mass. Mergers can also drive moderate star formation enhancements at lower redshifts (3 or 4 times at z = 1), but this accounts for only a few per cent of stellar mass in the dwarf regime given their infrequency. Non-merger interactions drive significantly smaller star formation enhancements (around two times), but their preponderance relative to mergers means they account for around 10 per cent of stellar mass formed in the dwarf regime.

Role of integrative medicine in the continuum of care of breast cancer patients in the Indian context

2021 ◽  
Author(s):  
Partha Basu ◽  
Richa Tripathi ◽  
Ravi Mehrotra ◽  
Koninika Ray ◽  
Anurag Srivastava ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Cancer Patients ◽  
Integrative Medicine ◽  
Continuum Of Care ◽  
Breast Cancer Patients ◽  
Indian Context ◽  
The Continuum

Moments of the Boltzmann collision operator for Coulomb interactions

2021 ◽  
Vol 28 (7) ◽  
pp. 072113
Author(s):  
Jeong-Young Ji ◽  
Min Uk Lee ◽  
Eric D. Held ◽  
Gunsu S. Yun
Keyword(s):  
Collision Operator ◽  
Coulomb Interactions ◽  
Boltzmann Collision Operator

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

Sign in / Sign up

Export Citation Format

Share Document