Session G19: General Fluid Dynamics I

Multiplicity and spatiotemporal pattern formation in subdiffusive autocatalytic systems

Many natural phenomena involving physical, chemical and biological processes are subdiffusive in nature. Mathematically these are governed by fractional-order differential equations. The mean square displacement of molecules here scale as ??^??, where 0<??<1. A two-variable system governed by a combination of quadratic and cubic autocatalytic reactions in a porous media is analysed in this work. Here each reactant is involved in the autocatalytic generation of the other. In this work, we investigate the effect of subdiffusion on the stability of the steady-states of the system. We use singularity theory to identify critical surfaces across which the bifurcation diagrams vary. We also develop a methodology in this paper to determine regions in parameter space where Turning patterns can be observed. This approach is based on identifying different critical surfaces across which steady-state stability changes when diffusive effects are included. The behaviour in the different regions is verified by a robust implicit numerical method developed for nonlinear systems based on the ??1 scheme. We find that subdiffusion or fractional-order effects increase the region of dynamic stability of a system. We show that for a subdiffusive system, the region in parameter space, which shows Turing patterns, increases.   

Ultra-high-speed imaging of laser-induced interfacial dynamics in superfluid and solid helium

Superfluid helium (He-II) becomes a solid at pressures of about 25 atmospheres. The interface between solid and the superfluid exhibits intriguing behavior, with wavy time-evolving oscillations on its surface (K. Keshishev, JETP Lett, 30. 1). It can thereby act similar to a free surface (S. Balibar, RevModPhys. 77. 1. 327). Herein, we use ultra-high-speed imaging at frame rates up to 7 million frames per second to experimentally investigate laser-induced interfacial dynamics at temperatures between 1.2 K and 2 K and at pressures starting from the melting pressure of about 25 atm and up to 39 atm, which spans both HCP and BCC structure of the solid.  The system (N. Speirs, PhysRevFluids. 5. 044001), has five optical windows which we use to pass the pulsed laser-beam through and capture the dynamics using ultra-high speed cameras, watching through a different set of windows. We use a 532 nm, pulsed Nd:YAG laser with a duration of ~ 6 ns and variable pulse energy up to 120 mJ to disturb the interface, focused by a parabolic mirror within the cell. We characterize melting and resolidification as well as track interface motions and shockwaves inside the different phases. 

    

The Generalized Newton's Laws (GNL) - A Complete Conformal Field Theory of Quantum Gravity

This paper will prove that the GNL theory on Quantum Gravity (QG) is a complete and robust Conformal Field Theory (CFT) as the Liouville CFT (LCFT). Here, I will directly from the standard LCFT induce to the complete GNL theory on Quantum Gravity. 

(1). Theorem 1.

Let S_L be the Liouville Action functional, in the case of the Riemann sphere, there exists a metric as: e^γφ(z) |dz|² and the law of φ is:

ν(dφ) = e^-S_L ν₀(dφ).                               (1)

then we can prove that this law is an isomorphism manifold with the Heat Kernel in the Unitary Space-Time of the GNL such as:

Ker= e^-x∗x/(2t)/√2πt. Hence these two CFT theories are an isomorphism map, in topological structures, specially.

 

(2). Theorem 2.

The LCFT has two parameters γ and μ, is characterized by its central charge: 

c_M = 25 - 6 Q²                                      (2)   

Q = 2/γ + γ/2.                                       (3)

hence if the central charge c_M = 0 and therefore to

γ = √(8/3) then we induce to a global topology on Quantum Gravity in the GNL:

GM 4(1- M²) = GM 4(1+ M)(1-M)         (4)

In normal cases, the Newton's gravity constant G = 2/3 = 0.666..., which leads to

8/3 M(1+ M)(1- M) = Id = 1.                  (5)

We clearly can use the parameters of the LCFT to lead to the main results on the relation between Mass and Velocity of the GNL:

V = 4(1- M²) = (2cos(φ))²= 4 cos²(φ)        (6)

and 

M = √(1 - V/4).                                                         (7)

(3). Theorem 3.

The GNL is a complele and exact Quantum Gravity theory, since it can give a global dynamics on Expansion and Retraction of the Universe and Fundamental Particle (Using Courant Algebroid):

2 ± √3 + 1/(2 ± √3) = 4.                                           (8)

and

2 ± √5  -  1/(2 ±√5) = 4.                                           (9)            

Finally, there exists an ergodic topological form of the quasi-stable light speed v = 3x ... km/s and the limit photon speed v_max= 4:

2n ± √3 + 1/(2n ±√3)  ↔   2n ± √5 - 1/(2n ± √5)     (10)

    

Performance improvement in soft robots by exploiting viscoelastic non-integer-order dynamical systems

Soft robots comprised of flexible materials, such as inflatable actuators and capacitive touch sensors, have recently gained attention for their capability to produce complex and adoptable motions through nonlinear deformation, simplistic synthesis, ease of fabrication, and low cost. A continuum soft body can be modeled as a high-dimensional, locally coupled nonlinear system. Soft robots are defined by their nonlinearity and the viscoelasticity of their soft components; these properties cannot be fully captured by ordinary linear differential equations without using many model parameters. The complex behavior of viscoelastic materials can be approximated with the classical Maxwell and Kelvin–Voigt models via many parameters, which dramatically limits model estimations and optimal design mechanisms. In this study, we propose a fractional model that captures complex viscoelastic behaviors with fewer parameters. We will present new insights for analyzing and designing complex soft robots by combining control theory, fluid dynamics, network science, and fractional-order calculus tools.   

Collisions of two particles in both lab and center of mass frame

We experimentally investigate the dynamics of two spherical particles free to collide in a vertically shaken channel. The identical particles both have a diameter of ??=5.0 ????. Multiple cases are considered for driving frequencies, f, ranging from 23 to 32 Hz and the acceleration magnitudes, Γ, from 1.78 to 3.53 g. The relative velocity and the total mechanical energy of the two particles before and after collisions are examined in both the lab frame and the center of mass frame. Super-elastic collisions, where the coefficient of restitution is measured to be greater than unity, are observed in this experiment. Most of the data suggest a slight mechanical energy loss during the collisions, and a linear fit is applied to obtain the coefficient of restitution between the two particles with a nearly constant value of approximately 0.8. The results of a simulation suggests that the super-elastic collisions result from an occasional mechanical energy transfer between the rotational and translational degrees of freedom.