Hamiltonian Frenet-Serret dynamics

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the Hamiltonian equations of motion are written down and a geometrical interpretation is provided for the canonical variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class. Quant. Gra

Covariant perturbations of domain walls in curved spacetime

A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0

Greater Istanbul metropolitan area planning experience (1965-1980)

Following the enforcement of the Urban Development Act in 1956 and the foundation of the Ministry of Reconstruction and Settlement in 1958, the first regional plan was developed for the Eastern Marmara Region in Turkey. The regional plan, which was prepared by the Ministry of Reconstruction and Settlement, in collaboration with the State Planning Office aimed at directing the industrial developments, the distribution of the industrial population and defining the hierarchy of urban settlements in the region respectively. The Regional Plan proposed an urban and regional infrastructure and a linear settlement development model for the Greater Istanbul area for the first time. The cities in Turkey were subject to a rapid urbanization due to a continuous flow of population from rural areas to the cities, which accelerated after 1950s. As a result, a multiplicity of new municipalities outside the existing limits of the major cities were formed, which necessitated a holistic planning in metropolitan scale. With this objective, three metropolitan planning offices were established for the major cities, Istanbul, Ankara and Izmir under the Ministry of Reconstruction and Settlement. In continuity with the principal decisions of the East Marmara Regional Plan, the planning studies for the Greater Metropolitan Area of Istanbul started with the foundation of Greater Istanbul Metropolitan Planning Office in 1965. The distribution of population between European and Asian sides of Istanbul metropolitan area was studied, and a linear pattern of settlement units separated by green areas was adopted in line with the regional plan. A strategic planning model was adopted in the last stage of the metropolitan planning. Based on an extensive survey, the demands of different sectors were defined. Alternative development strategies and scenarios were proposed with regard to the demands of the sectors. Beginning with the regional planning scale, the distribution of the residential and working areas, different strategies were tested with respect to their performances in achieving the initial development objectives. Based on an extensive data, projections, and regional development strategies updated, a plan that could guide the urban development policies was achieved. The metropolitan plan was completed and approved by the Ministry in July 1980. The Metropolitan Plan of Greater Istanbul constituted the first metropolitan plan, in Turkey, where the strategic planning approach was applied by comparing alternative development strategies. However, it could not be implemented properly as the planning authority was transferred to the Greater Municipality. Yet, with its holistic approach, this metropolitan plan that defined strategies of urban development and natural and urban conservation in metropolitan scale, could have prevented unplanned, piecemeal operations if it could be implemented. In the present paper, the metropolitan planning experience of Greater Istanbul is studied with a focus on the 1980 master plan. The role of the planning decisions in the urban development of the metropolitan city will be discussed at the end of the paper

The Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of solutions. We demonstrate that the proposed derivation of the Penrose inequality based on the Jang equation cannot work in the spherically symmetric case. Thus it is fruitless to apply this method, as it stands, to the general case. We show also that those analytic criteria for the formation of horizons that are based on the use of the Jang equation are of limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

Hamilton's equations for a fluid membrane: axial symmetry

Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: {\it (i)} the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space; {\it (ii)} the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.Comment: 11 page

Public behaviour in response to the Covid-19 pandemic: Understanding the role of group processes

Background In the absence of a vaccine, behaviour by the public is key to the response to the Covid-19 pandemic. Yet, as with other types of crises and emergencies, there have been doubts about the extent to which the public are able to engage effectively with the required behaviour. These doubts are based on outdated models of group psychology. Aims and argument We analyse the role of group processes in the Covid-19 pandemic in three domains: recognition of threat; adherence by the public to the required public health behaviours (and the factors that increase such adherence); and actions of the many community mutual aid groups that arose during lockdown. In each case, we draw upon the accumulated research on behaviour in emergencies and disasters as well as the latest findings in relation to the Covid-19 pandemic to show that explanations in terms of social identity processes make better sense of the patterns of evidence than alternative explanations. Conclusion If behaviour in the pandemic is a function of mutable group processes rather than fixed tendencies, then behavioural change is possible. There was evidence of significant change in behaviour from the public, particularly in the early days of the pandemic. Understanding the role of group processes means we can help design more effective interventions to support collective resilience in the public in the face of the pandemic and other threats. We draw out from the evidence a set of recommendations on facilitating the public response to Covid-19 by harnessing group processes

Axially symmetric membranes with polar tethers

Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c.If c\ne 0, a geometry with spherical topology will possess curvature singularities at its poles. The physical origin of the singularity is identified by examining the Noether charge associated with the translational invariance of the energy; it is consistent with an external axial force acting at the poles. A one-parameter family of exact solutions displaying a discocyte to stomatocyte transition is described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon equation for the shape of axi-symmetric membrane

Geometry of Deformations of Relativistic Membranes

A kinematical description of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations describing infinitesimal deformations about solutions of these equations when the action describing the dynamics of this membrane is constructed using {\it any} local geometrical worldsheet scalars. As examples, we consider a Nambu membrane, and an action quadratic in the extrinsic curvature of the worldsheet.Comment: 20 pages, Plain Tex, sign errors corrected, many new references added. To appear in Physical Review

Untethered micro-robotic coding of three-dimensional material composition

Complex functional materials with three-dimensional micro- or nano-scale dynamic compositional features are prevalent in nature. However, the generation of three-dimensional functional materials composed of both soft and rigid microstructures, each programmed by shape and composition, is still an unsolved challenge. Herein, we describe a method to code complex materials in three-dimensions with tunable structural, morphological, and chemical features using an untethered magnetic micro-robot remotely controlled by magnetic fields. This strategy allows the micro-robot to be introduced to arbitrary microfluidic environments for remote two- and three-dimensional manipulation. We demonstrate the coding of soft hydrogels, rigid copper bars, polystyrene beads, and silicon chiplets into three-dimensional heterogeneous structures. We also use coded microstructures for bottom-up tissue engineering by generating cell-encapsulating constructs

Cut-wire-pair structures as two-dimensional magnetic metamaterials

We study numerically and experimentally magnetic metamaterials based on cut-wire pairs instead of split-ring resonators. The cut-wire pair planar structure is extended in order to create a truly two-dimensional metamaterial suitable for scaling to optical frequencies. We fabricate the cut-wire metamaterial operating at microwave frequencies with lattice spacing around 10% of the free-space wavelength, and find good agreement with direct numerical simulations. Unlike the structures based on split-ring resonators, the nearest-neighbor coupling in cut-wire pairs can result in a magnetic stop-band with propagation in the transverse direction