Package-X: A Mathematica package for the analytic calculation of one-loop integrals

Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool.Comment: Package files are available at http://packagex.hepforge.or

Topologically protected elastic waves in phononic metamaterials

Topological states of quantum matter exhibit unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk. Such immunity from backscattering makes topological surface or edge states ideal carriers for both classical and quantum information. So far, topological matters have been explored only in the realms of electronics and photonics, with limited range of bulk properties and largely immutable materials. These constraints thus impose severe performance trade-offs in experimentally realizable topologically ordered states. In contrast, phononic metamaterials not only provide access to a much wider range of material properties, but also allow temporal modulation in the non-adiabatic regime. Here, from the first-principles we demonstrate numerically the first phononic topological metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A dual-scale phononic crystal slab is used to support two effective spins of phonon over a broad bandwidth, and strong spin-orbit coupling is realized by breaking spatial mirror symmetry. By preserving the spin polarization with an external load or spatial symmetry, phononic edge states are shown to be robust against scattering from discrete defects as well as disorders in the continuum. Our system opens up the possibility of realizing topological materials for phonons in both static and time-dependent regimes.Comment: 19 pages, 6 figure

State-recycling and time-resolved imaging in topological photonic lattices

Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as "time," accessing long timescales constitutes a severe experimental challenge. Here, we overcome this limitation by placing the photonic lattice in a cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon detector array, offers quasi-real time-resolved measurements after each round trip. We apply the state-recycling scheme to intriguing photonic lattices emulating Dirac fermions and Floquet topological phases. In this new platform, we also realise a synthetic pulsed electric field, which can be used to drive transport within photonic lattices. This work opens a new route towards the detection of long timescale effects in engineered photonic lattices and the realization of hybrid analogue-digital simulators.Comment: Comments are welcom

Complexity, rate, and scale in sliding friction dynamics between a finger and textured surface.

Sliding friction between the skin and a touched surface is highly complex, but lies at the heart of our ability to discriminate surface texture through touch. Prior research has elucidated neural mechanisms of tactile texture perception, but our understanding of the nonlinear dynamics of frictional sliding between the finger and textured surfaces, with which the neural signals that encode texture originate, is incomplete. To address this, we compared measurements from human fingertips sliding against textured counter surfaces with predictions of numerical simulations of a model finger that resembled a real finger, with similar geometry, tissue heterogeneity, hyperelasticity, and interfacial adhesion. Modeled and measured forces exhibited similar complex, nonlinear sliding friction dynamics, force fluctuations, and prominent regularities related to the surface geometry. We comparatively analysed measured and simulated forces patterns in matched conditions using linear and nonlinear methods, including recurrence analysis. The model had greatest predictive power for faster sliding and for surface textures with length scales greater than about one millimeter. This could be attributed to the the tendency of sliding at slower speeds, or on finer surfaces, to complexly engage fine features of skin or surface, such as fingerprints or surface asperities. The results elucidate the dynamical forces felt during tactile exploration and highlight the challenges involved in the biological perception of surface texture via touch

System theory as applied differential geometry

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented

Decoupled controllers for power systems

Imperial Users onl

Transferring structural knowledge across cognitive maps in humans and models

Relations between task elements often follow hidden underlying structural forms such as periodicities or hierarchies, whose inferences fosters performance. However, transferring structural knowledge to novel environments requires flexible representations that are generalizable over particularities of the current environment, such as its stimuli and size. We suggest that humans represent structural forms as abstract basis sets and that in novel tasks, the structural form is inferred and the relevant basis set is transferred. Using a computational model, we show that such representation allows inference of the underlying structural form, important task states, effective behavioural policies and the existence of unobserved state-trajectories. In two experiments, participants learned three abstract graphs during two successive days. We tested how structural knowledge acquired on Day-1 affected Day-2 performance. In line with our model, participants who had a correct structural prior were able to infer the existence of unobserved state-trajectories and appropriate behavioural policies