Supersymmetry algebras and Lorentz invariance for d=10 Super Yang-Mills

We consider ways in which conventional supersymmetry can be embedded in the set of more general fermionic transformations proposed recently [\Ref{B}] as a framework in which to study $d=10$ super Yang-Mills. Solutions are exhibited which involve closed algebras of various numbers of supersymmetries together with their invariance groups: nine supersymmetries with \GT {\times}\SO (1,1) invariance; eight supersymmetries with \SO (7){\times}\SO (1,1) invariance; four supersymmetries with \SO (3,1){\times}\U (3) invariance. We recover in this manner all previously known ways of adding finite numbers of bosonic auxiliary fields so as to partially close the $d=10$ superalgebra. A crucial feature of these solutions is that the auxiliary fields transform non-trivially under the residual Lorentz symmetry, even though they are originally introduced as Lorentz scalars.Comment: 11 pages, plain tex (macros included), CERN-TH.7231/9

Geometry and Dynamics with Time-Dependent Constraints

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.Comment: 8 pages, Plain TeX, CERN-TH.7392/94 and MPI-PhT/94-4

Making Memories: Why Time Matters

In the last decade advances in human neuroscience have identified the critical importance of time in creating long-term memories. Circadian neuroscience has established biological time functions via cellular clocks regulated by photosensitive retinal ganglion cells and the suprachiasmatic nuclei. Individuals have different circadian clocks depending on their chronotypes that vary with genetic, age, and sex. In contrast, social time is determined by time zones, daylight savings time, and education and employment hours. Social time and circadian time differences can lead to circadian desynchronization, sleep deprivation, health problems, and poor cognitive performance. Synchronizing social time to circadian biology leads to better health and learning, as demonstrated in adolescent education. In-day making memories of complex bodies of structured information in education is organized in social time and uses many different learning techniques. Research in the neuroscience of long-term memory (LTM) has demonstrated in-day time spaced learning patterns of three repetitions of information separated by two rest periods are effective in making memories in mammals and humans. This time pattern is based on the intracellular processes required in synaptic plasticity. Circadian desynchronization, sleep deprivation, and memory consolidation in sleep are less well-understood, though there has been considerable progress in neuroscience research in the last decade. The interplay of circadian, in-day and sleep neuroscience research are creating an understanding of making memories in the first 24-h that has already led to interventions that can improve health and learning

Models for sound propagation in suspensions and emulsions

Theoretical and experimental work on sound propagation in suspensions and emulsions is reviewed. Three theoretical approaches are identified: scattering theory, coupled phase theory and porous media theory. Coupled phase theory is extended and compared analytically and numerically to scattering and porous media theory. Important regimes of scattering theory - the lossless and viscothermal scattering, single and multiple scattering and incoherent scattering regimes - are examined. Experimental data is used to corroborate lossless multiple scattering theory in the short wavelength, high volume fraction region. Previous coupled phase theories have modelled sound propagation in two phase media (i) with heat transfer assuming incompressible particles and (ii) with a compressible particulate phase neglecting heat transfer. Type (i) models are examined analytically and compared to scattering theory. Types (i) and (ii) are compared and brought together in a more general coupled phase theory. The new theory provides an alternative model to scattering theory for sound propagation in emulsions. Predictions of the new theory are compared to experimental data and predictions of scattering theory. Conditions for the equivalence of the frameless Biot porous media theory and coupled phase theory are identified. Predictions of the two approaches are compared to experimental data. New measurements of pore size distribution are used to predict measured acoustical properties of air saturated glass beads. Other extensions to coupled phase theory are reviewed and developed. Predictions including the effect of high volume fraction on the drag and the induced mass force are compared to experimental data and predictions of porous media theory. Coupled phase theory including heat transfer is extended to include particle size distributions; predictions of tl-ds are compared to measurements. The effect of non-spherical particles is investigated. Using the theory of Culick, frequency shifts for modes in an enclosure into which a suspension has been introduced are calculated. These are compared to the predictions of an intuitive approach. The method of Margulies and Schwartz for modelling particle diffusion is discussed. Areas where further work is required are identified

Spacetime Supersymmetry in a nontrivial NS-NS Superstring Background

In this paper we consider superstring propagation in a nontrivial NS-NS background. We deform the world sheet stress tensor and supercurrent with an infinitesimal B_{\mu\nu} field. We construct the gauge-covariant super-Poincare generators in this background and show that the B_{\mu\nu} field spontaneously breaks spacetime supersymmetry. We find that the gauge-covariant spacetime momenta cease to commute with each other and with the spacetime supercharges. We construct a set of "magnetic" super-Poincare generators that are conserved for constant field strength H_{\mu\nu\lambda}, and show that these generators obey a "magnetic" extension of the ordinary supersymmetry algebra.Comment: 13 pages, Latex. Published versio

Measuring storage and loss moduli using optical tweezers: broadband microrheology

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalised Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers.Comment: 5 pages, 3 figure

Optical tweezers: wideband microrheology

Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and micro-litre volumes. Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the material's high-frequency response, discarding important information related to the low-frequency behavior, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalised Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off.Comment: 13 pages, 6 figures, submitted to Special Issue of the Journal of Optic