Steven D. Miller

activity

20212023

collaborators

6 papers

physics.flu-dyn2023

Second And Third-Order Structure Functions Of An 'Engineered' Random Field And Emergence Of The Kolmogorov 4/5 And 2/3-Scaling Laws Of Turbulence

Steven D Miller

The 4/5 and 2/3 laws of turbulence can emerge from a theory of 'engineered' random vector fields $X_{i} (x, t) = X_{i} (x, t) + \frac{θ}{d ( d + 2 )} X_{i} (x, t) ψ (x)$ existing w…

math.PR2023

A Cluster Expansion Proof That The Stochastic Exponential Of A Brownian Motion Is A Martingale

Steven D Miller

Let $ψ : R^{+} \to R^{+}$ be a smooth and continuous real function and $ψ \in L^{2} (R^{+})$ . Let $B (t)$ be a standard Brownian motion define…

math-ph2023

A Stochastic Differential Equation For Laser Propagation In Medias With Random Gaussian Absorption Coefficients: A Modified Beer's Law Solution Via A Van Kampen Cluster Expansion

Steven D Miller

Let $I D = [0, L] \subset R^{+}$ be a slab geometry with boundaries $z = 0$ and $z = L$ . A laser beam with a flat incident intensity $ψ_{o}$ enters the…

math-ph2022

A Turbulent Fluid Mechanics Via Nonlinear Mixing Of Smooth Velocity Flows With Reynolds-Weighted Random Fields

Steven D Miller

We consider a finite-volume domain $D \subset R^{3}$ of size $Vol (D) \sim L^{3}$ containing a viscous fluid of kinematic viscosity $ν$ …

gr-qc2021

The Fundamental Equilibrium Equation For Gaseous Stars And The Tolman-Oppenheimer-Volkoff Equation -- Derivations And Applications With Emphasis On Optimisational-Variational Methods

Steven D Miller

Stars are essentially gravitationally stabilised thermonuclear reactors in hydrostatic equilibrium. The fundamental differential equation for all Newtonian gaseous stars in equilib…

math.NT2021

On the Local-Global Conjecture for Commutator Traces

Brooke Logan Ogrodnik

We study the trace set of the commutator subgroup of $Γ (2),$ a type of Local-Global problem about thin groups. We determine the local obstructions and then use the correspondence b…