33 citations · 117 across the 13 of their papers we have counts for
13 papers
On the efficient numerical computation of covariant Lyapunov vectors
Jean-Jacq du Plessis, Malcolm Hillebrand, Charalampos Skokos
Covariant Lyapunov vectors (CLVs) are useful in multiple applications, but the optimal time windows needed to accurately compute these vectors are yet unclear. To remedy this, we i…
Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method
Bertin Many Manda, Malcolm Hillebrand, Charalampos Skokos
We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equ…
The evolution of the phase space structure along pitchfork and period-doubling bifurcations in a 3D galactic bar potential
Henok Tenaw Moges, Matthaios Katsanikas, Panos Patsis +2
We investigate how the phase space structure of a 3D autonomous Hamiltonian system evolves across a series of successive 2D and 3D pitchfork and period-doubling bifurcations, as th…
Navigating Phase Space Transport with the Origin-Fate Map
Malcolm Hillebrand, Matthaios Katsanikas, Stephen Wiggins +1
We introduce and demonstrate the usage of the origin-fate map (OFM) as a tool for the detailed investigation of phase space transport in reactant-product type systems. For these sy…
Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
Sebastian Zimper, Arnold Ngapasare, Malcolm Hillebrand +3
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with…
Bubble relaxation dynamics in homopolymer DNA sequences
Malcolm Hillebrand, George Kalosakas, Alan R Bishop +1
Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on hel…
Quantifying chaos using Lagrangian descriptors
Malcolm Hillebrand, Sebastian Zimper, Arnold Ngapasare +3
We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on…
Bubble lifetimes in DNA gene promoters and their mutations affecting transcription
M Hillebrand, G Kalosakas, A R Bishop +1
Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either incre…
Chaotic Dynamics of Polyatomic Systems with an Emphasis on DNA Models
Malcolm Hillebrand
We investigate the chaotic behaviour of multiparticle systems, in particular DNA and graphene models, by applying methods of nonlinear dynamics. Using symplectic integration techni…
Distributions of Bubble Lifetimes and Bubble Lengths in DNA
Malcolm Hillebrand, George Kalosakas, Haris Skokos +1
We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-…
Chaotic dynamics of graphene and graphene nanoribbons
Malcolm Hillebrand, Bertin Many Manda, George Kalosakas +2
We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically cal…
Heterogeneity and chaos in the Peyrard-Bishop-Dauxois DNA model
Malcolm Hillebrand, George Kalosakas, Adrian Schwellnus +1
We discuss the effect of heterogeneity on the chaotic properties of the Peyrard-Bishop-Dauxois nonlinear model of DNA. Results are presented for the maximum Lyapunov exponent and t…
Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Polya Counting to a Physical System
Malcolm Hillebrand, Guy Paterson-Jones, George Kalosakas +1
In modeling DNA chains, the number of alternations between Adenine-Thymine (AT) and Guanine-Cytosine (GC) base pairs can be considered as a measure of the heterogeneity of the chai…