Evan Camrud

• Ph.D. Mathematics
• Postdoctoral Fellow at Colorado State University

It is well recognized that interpreting transport experiment results can be challenging when the samples being measured are spatially nonuniform. However, quantitative understanding on the differences between measured and actual transport coefficients, especially the Hall effects, in inhomogeneous systems is lacking. In this work we use homogenizat...

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses the unadjusted Hamiltonian Monte Carlo method. Assuming that the target distribution $\pi$ satisfies a log-So...

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential U allowing for singularities. By modifying the direct approach to convergence in L ² pioneered by Hérau and developed by Dolbeault et al , we show that the dynamics converges exponentially fast to equilibrium in the topologies L ² (d μ...

Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Can...

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential $U$ allowing for singularities. By modifying the direct approach to convergence in $L^2$ pioneered by F. H\'erau and developped by Dolbeault, Mouhot and Schmeiser, we show that the dynamics converges exponentially fast to equilibrium in...

Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Cantor set can be rec...

The Kaczmarz algorithm is an iterative method to reconstruct an unknown vector f from inner products \(\langle f , \varphi _{n} \rangle \). We consider the problem of how additive noise affects the reconstruction under the assumption that \(\{ \varphi _{n} \}\) form a stationary sequence. Unlike other reconstruction methods, such as frame reconstru...

Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct non-integer powers of operators. In doing so, we not only provide a more intuitive understanding of fractional theories...

The Kaczmarz algorithm is an iterative method to reconstruct an unknown vector $f$ from inner products $\langle f , \varphi_{n} \rangle $. We consider the problem of how additive noise affects the reconstruction under the assumption that $\{ \varphi_{n} \}$ form a stationary sequence. Unlike other reconstruction methods, such as frame reconstructio...

The purpose of this work is to show that the Khalil and Katagampoula conformable derivatives are equivalent to the simple change of variables x → x α /α, where α is the order of the derivative operator, when applied to differential functions. Although this means no "new mathematics" is obtained by working with these derivatives, it is a second purp...

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants of integration in their results. An elimination of constants of integration opens the door to an operator that...

A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as such paves a way for application to many other areas of analysis involving distributions. This includes (but is n...

Numerous computational and spectroscopic studies have demonstrated the decisive role played by nonadiabatic coupling in photochemical reactions. Nonadiabatic coupling drives photochemistry when potential energy surfaces are nearly degenerate at avoided crossings or truly degenerate at unavoided crossings. The dynamics induced by nonadiabatic coupli...