Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is consistent with another solitary peakon solution. By reversing the time, we get two new solutions with the same initial value and different values at the rest of the time, which means the nonuniqueness for the equation in Sobolev spaces H s is proved for s < 3 / 2 .

Numerical Study of Electrostatic Desalting Process Based on Droplet Collision Time

The desalting process of an electrostatic desalting unit was studied using the collision time of two droplets in a water-in-oil (W/O) emulsion based on force balance. Initially, the model was solved numerically to perform a process analysis and to indicate the effect of the main process parameters, such as electric field strength, water content, temperature (through oil viscosity) and droplet size on the collision time or frequency of collision between a pair of droplets. In decreasing order of importance on the reduction of collision time and consequently on the efficiency of desalting separation, the following variables can be classified such as moisture content, electrostatic field strength, oil viscosity and droplet size. After this analysis, a computational fluid dynamics (CFD) model of a biphasic water–oil flow was developed in steady state using a Eulerian multiphase framework, in which collision frequency and probability of coalescence of droplets were assumed. This study provides some insights into the heterogeneity of a desalination plant which highlights aspects of design performance. This study further emphasizes the importance of two variables as moisture content and intensity of electrostatic field for dehydrated desalination by comparing the simulation with the electrostatic field against the same simulation without its presence. The overall objective of this study is therefore to show the necessity of including complex phenomena such as the frequency of collisions and coalescence in a CFD model for better understanding and optimization of the desalting process from both process safety and improvement.

Roaming pathways and survival probability in real-time collisional dynamics of cold and controlled bialkali molecules

Perfectly controlled molecules are at the forefront of the quest to explore chemical reactivity at ultra low temperatures. Here, we investigate for the first time the formation of the long-lived intermediates in the time-dependent scattering of cold bialkali $$^{23}\hbox {Na}^{87}$$ 23 Na 87 Rb molecules with and without the presence of infrared trapping light. During the nearly 50 nanoseconds mean collision time of the intermediate complex, we observe unconventional roaming when for a few tens of picoseconds either NaRb or $$\hbox {Na}_2$$ Na 2 and $$\hbox {Rb}_2$$ Rb 2 molecules with large relative separation are formed before returning to the four-atom complex. We also determine the likelihood of molecular loss when the trapping laser is present during the collision. We find that at a wavelength of 1064 nm the $$\hbox {Na}_2\hbox {Rb}_2$$ Na 2 Rb 2 complex is quickly destroyed and thus that the $$^{23}\hbox {Na}^{87}$$ 23 Na 87 Rb molecules are rapidly lost.

Wavelength scaling of electron collision time in plasma for strong field laser-matter interactions in solids

Although the dielectric constant of plasma depends on electron collision time as well as wavelength and plasma density, experimental studies on the electron collision time and its effects on laser-matter interactions are lacking. Here, we report an anomalous regime of laser-matter interactions generated by wavelength dependence (1.2–2.3 µm) of the electron collision time in plasma for laser filamentation in solids. Our experiments using time-resolved interferometry reveal that electron collision times are small (<1 femtosecond) and decrease as the driver wavelength increases, which creates a previously-unobserved regime of light defocusing in plasma: longer wavelengths have less plasma defocusing. This anomalous plasma defocusing is counterbalanced by light diffraction which is greater at longer wavelengths, resulting in almost constant plasma densities with wavelength. Our wavelength-scaled study suggests that both the plasma density and electron collision time should be systematically investigated for a better understanding of strong field laser-matter interactions in solids.

Dynamical symmetrization of the state of identical particles

We propose a dynamical model for state symmetrization of two identical particles produced in spacelike-separated events by independent sources. We adopt the hypothesis that the pair of non-interacting particles can initially be described by a tensor product state since they are in principle distinguishable due to their spacelike separation. As the particles approach each other, a quantum jump takes place upon particle collision, which erases their distinguishability and projects the two-particle state onto an appropriately (anti-)symmetrized state. The probability density of the collision times can be estimated quasi-classically using the Wigner functions of the particles’ wavepackets, or derived from fully quantum mechanical considerations using an appropriately adapted time-of-arrival operator. Moreover, the state symmetrization can be formally regarded as a consequence of the spontaneous measurement of the collision time. We show that symmetric measurements performed on identical particles can in principle discriminate between the product and symmetrized states. Our model and its conclusions can be tested experimentally.

Coulomb collisions in strongly anisotropic plasmas I. Cyclotron cooling in electron–ion plasmas

The behaviour of a collisional plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various time scales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collision frequency multiplied by a factor that only depends logarithmically on plasma parameters.

Right Atrial Collision Time (RACT): a novel marker of propensity for typical atrial flutter

Background The risk of typical atrial flutter (AFL) is increased by factors that increase right atrial (RA) size or cause scarring to reduce conduction velocity. These characteristics ensure the macro re-entrant wave front does not meet its refractory tail. The time taken to traverse the circuit would take account of both of these characteristics (being equal to distance divided by velocity), and may provide a superior marker of propensity to develop AFL. Purpose To investigate right atrial collision time (RACT) as a marker of typical AFL. Methods This single centre, prospective study recruited consecutive typical AFL ablation cases that were in sinus rhythm. Controls were consecutive cases other than atrial fibrillation and &gt;50 years of age. Exclusion criteria for both groups were a prior ablation in the RA and class I and III antiarrhythmics. While pacing the coronary sinus ostium at 600 ms, a local activation time map was created to locate the latest collision point on the anterolateral wall, excluding the RA appendage (Figure 1). This RACT approximates half a revolution. Results The AFL group's (n=34) mean RACT was 132.5±15.06 vs 98.7±12.23ms in the controls (n=40) (p&lt;0.01). No significant difference was observed for age (mean 65.6 vs 62.6 (p=0.18)), male (68.8% vs 60% (p=0.59)), body surface area (mean 2.1 vs 2.03 m2 (p=0.24)). The RACT also proved to be a superior marker than the echocardiographic measurement of right atrial area in an apical four chamber view (mean 17.8 vs 16.3 cm2 (p=0.21).A ROC curve indicated an AUC of 0.97 (95% CI: 0.93–1.0, p&lt;0.01). A RACT cut-off of 120 ms had a specificity of 99% and a sensitivity of 75%. Conclusion RACT is a novel and promising marker of propensity for typical AFL. The ability to predict AFL would be of significant clinical value given the risk of stroke and frequent need for ablation. Funding Acknowledgement Type of funding source: None