Microscale simulations of shock interaction with large assembly of particles for developing point-particle models

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

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The kinematics of a point particle

10.1093/oso/9780198786399.003.0020 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Internal Structure ◽

Proper Time ◽

World Line ◽

Point Particle ◽

Material Point ◽

Spatial Extent ◽

Geometric Representation ◽

Mathematical Result ◽

Point Particles ◽

The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

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Shock interactions in inviscid air and $$\hbox {CO}_2$$–$$\hbox {N}_2$$ flows in thermochemical non-equilibrium

Shock Waves ◽

10.1007/s00193-021-00999-8 ◽

2021 ◽

Author(s):

C. Garbacz ◽

W. T. Maier ◽

J. B. Scoggins ◽

T. D. Economon ◽

T. Magin ◽

...

Keyword(s):

Chemical Species ◽

High Energy ◽

Ideal Gas ◽

Shock Interaction ◽

Interaction Patterns ◽

Shock Interactions ◽

Wave Interference ◽

Type V ◽

The Impact ◽

Non Equilibrium

AbstractThe present study aims at providing insights into shock wave interference patterns in gas flows when a mixture different than air is considered. High-energy non-equilibrium flows of air and $$\hbox {CO}_2$$ CO 2 –$$\hbox {N}_2$$ N 2 over a double-wedge geometry are studied numerically. The impact of freestream temperature on the non-equilibrium shock interaction patterns is investigated by simulating two different sets of freestream conditions. To this purpose, the SU2 solver has been extended to account for the conservation of chemical species as well as multiple energies and coupled to the Mutation++ library (Multicomponent Thermodynamic And Transport properties for IONized gases in C++) that provides all the necessary thermochemical properties of the mixture and chemical species. An analysis of the shock interference patterns is presented with respect to the existing taxonomy of interactions. A comparison between calorically perfect ideal gas and non-equilibrium simulations confirms that non-equilibrium effects greatly influence the shock interaction patterns. When thermochemical relaxation is considered, a type VI interaction is obtained for the $$\hbox {CO}_2$$ CO 2 -dominated flow, for both freestream temperatures of 300 K and 1000 K; for air, a type V six-shock interaction and a type VI interaction are obtained, respectively. We conclude that the increase in freestream temperature has a large impact on the shock interaction pattern of the air flow, whereas for the $$\hbox {CO}_2$$ CO 2 –$$\hbox {N}_2$$ N 2 flow the pattern does not change.

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The Little-Bang and the femto-nova in nucleus-nucleus collisions

AAPPS Bulletin ◽

10.1007/s43673-021-00002-7 ◽

2021 ◽

Vol 31 (1) ◽

Author(s):

Nu Xu ◽

Kenji Fukushima ◽

Bedangadas Mohanty

Keyword(s):

Collision Energy ◽

Particle Production ◽

Gluon Plasma ◽

Baryon Density ◽

Point Particle ◽

Current Status ◽

Density Region ◽

Qcd Critical Point ◽

Qcd Phase Diagram ◽

Lower Collision Energy

AbstractWe make a theoretical and experimental summary of the state-of-the-art status of hot and dense QCD matter studies on selected topics. We review the Beam Energy Scan program for the QCD phase diagram and present the current status of the search for the QCD critical point, particle production in high baryon density region, hypernuclei production, and global polarization effects in nucleus-nucleus collisions. The available experimental data in the strangeness sector suggests that a grand canonical approach in the thermal model at high collision energy makes a transition to the canonical ensemble behavior at low energy. We further discuss future prospects of nuclear collisions to probe properties of baryon-rich matter. Creation of a quark-gluon plasma at high temperature and low baryon density has been called the “Little-Bang” and, analogously, a femtometer-scale explosion of baryon-rich matter at lower collision energy could be called the “femto-nova”, which could possibly sustain substantial vorticity and a magnetic field for non-head-on collisions.

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Progenitors and Hydrodynamics of Type II and lb Supernovae

International Astronomical Union Colloquium ◽

10.1017/s0252921100008009 ◽

1996 ◽

Vol 145 ◽

pp. 137-147

Author(s):

S. E. Woosley ◽

T. A. Weaver ◽

R. G. Eastman

Keyword(s):

Black Holes ◽

Light Curve ◽

Mass Loss ◽

Massive Stars ◽

The Other ◽

Shock Interaction ◽

Type Ii ◽

Residual Hydrogen ◽

Ordinary Type ◽

The One

We review critical physics affecting the observational characteristics of those supernovae that occur in massive stars. Particular emphasis is given to 1) how mass loss, either to a binary companion or by a radiatively driven wind, affects the type and light curve of the supernova, and 2) the interaction of the outgoing supernova shock with regions of increasing pr3 in the stellar mantle. One conclusion is that Type II-L supernovae may occur in mass exchanging binaries very similar to the one that produced SN 1993J, but with slightly larger initial separations and residual hydrogen envelopes (∼1 Mʘ and radius ∼ several AU). The shock interaction, on the other hand, has important implications for the formation of black holes in explosions that are, near peak light, observationally indistinguishable from ordinary Type II-p and lb supernovae.

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