# Recent Publications

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In this modern and distinctive textbook, Helliwell and Sahakian present classical mechanics as a thriving and contemporary field with strong connections to cutting-edge research topics in physics. Each part of the book concludes with a capstone chapter describing various key topics in quantum mechanics, general relativity, and other areas of modern physics, clearly demonstrating how they relate to advanced classical mechanics, and enabling students to appreciate the central importance of classical mechanics within contemporary fields of research. Numerous and detailed examples are interleaved with theoretical content, illustrating abstract concepts more concretely. Extensive problem sets at the end of each chapter further reinforce students' understanding of key concepts, and provide opportunities for assessment or self-testing. A detailed online solutions manual and lecture slides accompany the text for instructors. Often a flexible approach is required when teaching advanced classical mechanics, and, to facilitate this, the authors have outlined several paths instructors and students can follow through the book, depending on background knowledge and the length of their course.

It was shown in a recent paper [J. Math. Phys. (N.Y.) 60, 102502 (2019)] that slowly lowering an electric charge into a Schwarzschild-Tangherlini (ST) black hole endows the final state with electric multipole fields, which implies that the final-state geometry is not Reissner-Nordström-Tangherlini in nature. This conclusion departs from the four-dimensional case in which the no-hair theorem (NHT) requires the final state to be a Reissner-Nordström black hole. To better understand this discrepancy clearly requires a deeper understanding of the origin of the multipole hair in the higher-dimensional case. In this paper, we advance the conjecture that charged, static, and asymptotically flat higher-dimensional black holes can acquire electric multipole hair only after they form. This supposition derives from studying the asymptotic behavior of the field of a multipole charge onto which a massive and hyperspherical shell with an exterior ST geometry is collapsing. In the mathematical limit as the shell approaches its ST radius, we find that the multipole fields (except the monopole) vanish. This implies that the only information of an arbitrary (but finite) charge distribution inside the collapsing shell that is available to an asymptotic observer is the total electric charge. Our results yield considerable insight into how higher-dimensional black holes acquire electric multipole hair, and also imply that, in four dimensions, the fadeaway of multipole moments during gravitational collapse is not strictly because of the NHT.

We propose a simple model in which the baryon asymmetry and dark matter are created via the decays and inverse decays of QCD-triplet scalars, at least one of which must be in the TeV mass range. Singlet fermions produced in these decays constitute the dark matter. The singlets never reach equilibrium, and their coherent production, propagation, and annihilation generates a baryon asymmetry. We find that the out-of-equilibrium condition and the dark matter density constraint typically require the lightest scalar to be long-lived, giving good prospects for detection or exclusion in current and upcoming colliders. In generalizing the leptogenesis mechanism of Akhmedov, Rubakov and Smirnov, our model expands the phenomenological possibilities for low-scale baryogenesis.

We carried out six targeted structure from motion surveys using small uninhabited aerial systems over the \( M_w \) 6.4 and 7.1 ruptures of the Ridgecrest earthquake sequence in the first three months after the events. The surveys cover approximately 500 \( \times \) 500 m areas just south of Highway 178 with an average ground sample distance of 1.5 cm. The first survey took place five days after the \( M_w \) 6.4 foreshock on 9 July 2019. The final survey took place on 27 September 2019. The time between surveys increased over time, with the first five surveys taking place in the first month after the earthquake. Comparison of imagery from before and after the \( M_w \) 7.1 earthquake shows variation in slip on the main rupture and a small amount of distributed slip across the scene. Cracks can be observed and mapped in the high-resolution imagery, which show en echelon cracking, fault splays, and a northeast-striking conjugate fault at the \( M_w \) 7.1 rupture south of Highway 178 and near the dirt road. Initial postseismic results show little fault afterslip, but possible subsidence in the first 7–10 days after the earthquake, followed by uplift.

Biological membranes are composed of lipid bilayers that are often asymmetric with regards to the lipid composition and/or aqueous solvent they separate. Studying lipid asymmetry both experimentally and computationally is challenging. Molecular dynamics simulations of lipid bilayers with asymmetry are difficult due to finite system sizes and time scales accessible to simulations. Due to the very slow flip-flop rate for phospholipids, one must first choose how many lipids are on each side of the bilayer, but the resulting bilayer may be unstable (or metastable) due to differing tensile and compressive forces between leaflets. Here we use molecular dynamics simulations to investigate a number of different asymmetric membrane systems, both with atomistic and coarse-grained models. Asymmetries studied include differences in number of lipids, lipid composition (unsaturated and saturated tails and different headgroups), and chemical gradients between the aqueous phases. Extensive analysis of the bilayers’ properties such as area per lipid, density, and lateral pressure profiles are used to characterize bilayer asymmetry. We also address how cholesterol (which flip-flops relatively quickly) influences membrane asymmetries. Our results show how each leaflet is influenced by the other and can mitigate the structural changes to the bilayer overall structure. Cholesterol can respond to changes in bilayer asymmetry to alleviate some of the effect on the bilayer structure, but that will alter its leaflet distribution, which in turn affects its chemical potential. Ionic imbalances are shown to have a modest change in bilayer structure, despite large changes in the electrostatic potential. Bilayer asymmetry can also induce a modest electrostatic potential across the membrane. Our results highlight the importance of membrane asymmetry on bilayer properties, the influence of lipid headgroups, tails and cholesterol on asymmetry, and the ability of lipids to adapt to different environments.

The inherent force–velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compression in one state and allow the spring to release energy without constraint in the other. Using a mathematical model of a simplified contact latch, we reproduce this instantaneous release behaviour and also demonstrate that changing latch parameters (latch release velocity and radius) can reduce and delay the energy released by the spring. We identify a critical threshold between instantaneous and delayed release that depends on the latch, spring, and mass of the system. Systems with stiff springs and small mass can attain a wide range of output performance, including instantaneous behaviour, by changing latch release velocity. We validate this model in both a physical experiment as well as with data from the Dracula ant, Mystrium camillae, and propose that latch release velocity can be used in both engineering and biological systems to control energy output.

We study the field of an electric point charge that is slowly lowered into an \( n + 1 \) dimensional Schwarzschild-Tangherlini black hole. We find that if \( n > 3 \), then countably infinite nonzero multipole moments manifest to observers outside the event horizon as the charge falls in. This suggests the final state of the black hole is not characterized by a Reissner-Nordström-Tangherlini geometry. Instead, for odd \( n \), the final state either possesses a degenerate horizon, undergoes a discontinuous topological transformation during the infall of the charge, or both. For even \( n \), the final state is not guaranteed to be asymptotically flat.

Charge order is now accepted as an integral constituent of cuprate high-temperature superconductors, one that is intimately related to other electronic instabilities including anti-ferromagnetism and superconductivity. Unlike conventional Peierls density waves, the charge correlations in cuprates have been predicted to display a rich momentum space topology depending on the underlying fermiology. However, charge order has only been observed along the high-symmetry Cu–O bond directions. Here, using resonant soft X-ray scattering, we investigate the evolution of the full momentum space topology of charge correlations in \( T'-\mathrm{(Nd,Pr)_2 CuO_4} \) as a function of electron doping. We report that, when the parent Mott insulator is doped, charge correlations first emerge with full rotational symmetry in momentum space, indicating glassy charge density modulation in real space possibly seeded by local defects. At higher doping levels, the orientation of charge correlations is locked to the Cu–O bond directions, restoring a more conventional long-ranged bidirectional charge order. Through charge susceptibility calculations, we reproduce the evolution in topology of charge correlations across the antiferromagnetic phase boundary and propose a revised phase diagram of \( T'-\mathrm{Ln_2 CuO_4} \) with a superconducting region extending toward the Mott limit.

The discovery of quantum oscillations in hole- and electron-doped cuprate families has underscored the importance of the Fermi surface in cuprate superconductivity. While the observed quantum oscillations in both families have revealed the presence of reconstructed Fermi surfaces, there remains an important distinction between the two. In hole-doped cuprates the oscillations are thought to arise from the effects of a charge density wave, while in the electron-doped cuprates it is thought that these oscillations occur from an antiferromagnetically reconstructed Fermi surface, despite the fact that the oscillations are observed in overdoped compounds, far from the putative antiferromagnetic critical point. In this work we study thin films of \( \mathrm{Pr_2 Cu O_{4 \pm \delta}} \), whose apparent doping can be finely tuned by annealing, allowing studies of quantum oscillations in samples straddling the critical point. We show that even though there is a mass enhancement of the quasiparticles, there are only small changes to the Fermi surface itself, suggesting that charge order is a more likely origin, with electronic correlations that are strongly dependent on the structural parameters.

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