scholarly journals Correction to “Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark”

2018 ◽  
Vol 9 (7) ◽  
pp. 1527-1527
Author(s):  
Carla Andreani ◽  
Giovanni Romanelli ◽  
Roberto Senesi
Keyword(s):  
Kinetic Energy ◽  
Triple Point ◽  
Energy Tensor ◽  
Direct Measurements ◽  
Metastable Water

scholarly journals Direct measurements of the mean flow and eddy kinetic energy structure of the upper ocean circulation in the NE Atlantic

2005 ◽  
Vol 32 (14) ◽  
pp. n/a-n/a ◽  
Author(s):  
Øyvind Knutsen ◽  
Harald Svendsen ◽  
Svein Østerhus ◽  
Tom Rossby ◽  
Bogi Hansen
Keyword(s):  
Kinetic Energy ◽  
Ocean Circulation ◽  
Eddy Kinetic Energy ◽  
Upper Ocean ◽  
Energy Structure ◽  
Mean Flow ◽  
Ne Atlantic ◽  
Direct Measurements ◽  
The Mean

scholarly journals A laboratory study of the retarding effects of braking mounds on snow avalanches

2003 ◽  
Vol 49 (165) ◽  
pp. 191-200 ◽  
Author(s):  
Kristín Martha Hákonardóttir ◽  
Andrew J. Hogg ◽  
Tómas Jóhannesson ◽  
Gunnar G. Tómasson
Keyword(s):  
Kinetic Energy ◽  
Granular Flow ◽  
Laboratory Experiments ◽  
Transverse Direction ◽  
Large Fraction ◽  
Snow Avalanches ◽  
Flow Depth ◽  
Retarding Effect ◽  
Direct Measurements ◽  
Mean Diameter

AbstractA series of laboratory experiments in a 6 m long chute using glass particles of mean diameter 100 μm were performed to investigate the interaction of a supercritical, granular flow with obstacles. It was found that the collision of the flow with a row of mounds led to the formation of a jet, whereby a large fraction of the flow was launched from the top of the mounds and subsequently landed back on the chute. The retarding effect of the mounds was investigated quantitatively by direct measurements of the velocity of the flow, its runout length and the geometry of the jet. The effects of several aspects of the layout of the mounds on their retarding effects were examined. It was observed that a row of steep mounds with an elongated shape in the transverse direction to the flow and with a height several times the flow depth led to dissipation of a large proportion of the kinetic energy of the flow.

scholarly journals The physics of temperature

2020 ◽  
pp. S55-S58
Author(s):  
BM Gardner
Keyword(s):  
Heat Capacity ◽  
Kinetic Energy ◽  
Specific Heat ◽  
Specific Heat Capacity ◽  
Triple Point ◽  
Heat Energy ◽  
The Body ◽  
Absolute Zero ◽  
Triple Point Of Water ◽  
Standard Pressure

Heat: a measure of the total kinetic energy of a body. Measured in joules (J). It depends on the mass of the body and the specific heat capacity of the body. Temperature: a measure of the average kinetic energy within a body. It describes the potential for heat energy to move from one body to another down a gradient from an area of high temperature to an area of lower temperature. It is measured using a temperature scale which is defined against fixed physical events such as absolute zero or the triple point of water. Heat capacity: the amount of heat energy necessary to be added to an entire body to increase the temperature by one degree Kelvin (J/K). Specific heat capacity: the amount of heat energy necessary to be added to one kilogram of a body to increase the temperature by one degree Kelvin (J/K/kg). Absolute zero: a hypothetical temperature at which all molecular movement stops (zero kinetic energy). This is not possible in reality. The ice point: this is the temperature at standard pressure (101.3 kPa) at which water exists in both a solid (ice) and a liquid form. Designated as 0 oC or 32 oF. The steam point (boiling point): the temperature at standard pressure (101.3 kPa) at which water exists in botha liquid and a vapour form. Designated as 100 oC or 212 oF. Triple point of water: the temperature at a pressure of 611 Pa (0.006 atm) at which water exists in a solid (ice), liquid and a vapour form. Designated as 0.01 oC.

A kinetic-based hyperbolic two-fluid model for binary hard-sphere mixtures

2019 ◽  
Vol 877 ◽  
pp. 282-329 ◽  
Author(s):  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Hard Sphere ◽  
Fluid Model ◽  
Kinetic Equations ◽  
Energy Tensor ◽  
Spatial Gradients ◽  
Phase Temperature ◽  
The Mean ◽  
Two Fluid Model ◽  
Two Fluid

Starting from coupled Boltzmann–Enskog (BE) kinetic equations for a two-particle system consisting of hard spheres, a hyperbolic two-fluid model for binary, hard-sphere mixtures is derived with separate mean velocities and energies for each phase. In addition to spatial transport, the BE kinetic equations account for particle–particle collisions, using an elastic hard-sphere collision model, and the Archimedes (buoyancy) force due to spatial gradients of the pressure in each phase, as well as other forces involving spatial gradients (e.g. lift). In the derivation, the particles in a given phase have identical mass and volume, and have no internal degrees of freedom (i.e. the particles are adiabatic). The ‘hard-sphere-fluid’ phase is obtained in the limit where the particle diameter in one phase tends to zero with fixed phase density so that the number of fluid particles tends to infinity. The moment system resulting from the two BE kinetic equations is closed at second order by invoking the anisotropic Gaussian closure. The resulting two-fluid model for a binary, hard-sphere mixture therefore consists (for each phase $\unicode[STIX]{x1D6FC}=1,2$) of transport equations for the mass $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}$, mean momentum $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}$ (where $\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}$ is the velocity) and a symmetric, second-order, kinetic energy tensor $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\unicode[STIX]{x1D640}_{\unicode[STIX]{x1D6FC}}=\frac{1}{2}\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}(\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}\otimes \boldsymbol{u}_{\unicode[STIX]{x1D6FC}}+\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}})$. The trace of the fluctuating energy tensor $\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}}$ is $\text{tr}(\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}})=3\unicode[STIX]{x1D6E9}_{\unicode[STIX]{x1D6FC}}$ where $\unicode[STIX]{x1D6E9}_{\unicode[STIX]{x1D6FC}}$ is the phase temperature (or granular temperature). Thus, $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}E_{\unicode[STIX]{x1D6FC}}=\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\text{tr}(\unicode[STIX]{x1D640}_{\unicode[STIX]{x1D6FC}})$ is the total kinetic energy, the sum over $\unicode[STIX]{x1D6FC}$ of which is the total kinetic energy of the system, a conserved quantity. From the analysis, it is found that the BE finite-size correction leads to exact phase pressure (or stress) tensors that depend on the mean-slip velocity $\boldsymbol{u}_{12}=\boldsymbol{u}_{1}-\boldsymbol{u}_{2}$, as well as the phase temperatures for both phases. These pressure tensors also appear in the momentum-exchange terms in the mean momentum equations that produce the Archimedes force, as well as drag contributions due to fluid compressibility and a lift force due to mean fluid-velocity gradients. The closed BE energy flux tensors show a similar dependence on the mean-slip velocity. The characteristic polynomial of the flux matrix from the one-dimensional model is computed symbolically and depends on five parameters: the particle volume fractions $\unicode[STIX]{x1D711}_{1}$, $\unicode[STIX]{x1D711}_{2}$, the phase density ratio ${\mathcal{Z}}=\unicode[STIX]{x1D70C}_{f}/\unicode[STIX]{x1D70C}_{p}$, the phase temperature ratio $\unicode[STIX]{x1D6E9}_{r}=\unicode[STIX]{x1D6E9}_{2}/\unicode[STIX]{x1D6E9}_{1}$ and the mean-slip Mach number $Ma_{s}=\boldsymbol{u}_{12}/\sqrt{5\unicode[STIX]{x1D6E9}_{1}/3}$. By applying Sturm’s Theorem to the characteristic polynomial, it is demonstrated that the model is hyperbolic over a wide range of these parameters, in particular, for the physically most relevant values.

scholarly journals Numerical Experiments on the Tensor Virial in N-Body Systems

1975 ◽  
Vol 69 ◽  
pp. 65-72
Author(s):  
R. H. Miller
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Numerical Experiments ◽  
Virial Theorem ◽  
Energy Tensor ◽  
Correlation Times ◽  
Crossing Time

Tensor generalizations of the virial theorem were checked in a 100-body integration. The virial theorem was remarkably well satisfied, and the calculation confirmed the generalized Lagrange-Jacobi identities. The potential energy tensor, the kinetic energy tensor, and the virial tensor showed surprisingly long correlation times of about of a crossing time.

Sign in / Sign up

Export Citation Format

Share Document