10,959 research outputs found
The non-zero energy of 2+1 Minkowski space
We compute the energy of 2+1 Minkowski space from a covariant action
principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic
flatness, we first show that the 2+1 Einstein-Hilbert action with
Gibbons-Hawking boundary term is both finite on-shell (apart from past and
future boundary terms) and stationary about solutions under arbitrary smooth
asymptotically flat variations of the metric. Thus, this action provides a
valid variational principle and no further boundary terms are required. We then
obtain the gravitational Hamiltonian by direct computation from this action.
The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an
overall addititve constant. This constant is such that 2+1 Minkowski space is
assigned the energy E = -1/4G, while the upper bound on the energy is set to
zero. Any variational principle with a boundary term built only from the
extrinsic and intrinsic curvatures of the boundary is shown to lead to the same
result. Interestingly, our result is not the flat-space limit of the
corresponding energy -1/8G of 2+1 anti-de Sitter space.Comment: 16 pages, minor change
First-passage time of run-and-tumble particles
We solve the problem of first-passage time for run-and-tumble particles in
one dimension. Exact expression is derived for the mean first-passage time in
the general case, considering external force-fields and chemotactic-fields,
giving rise to space dependent swim-speed and tumble rate. Agreement between
theoretical formulae and numerical simulations is obtained in the analyzed case
studies -- constant and sinusoidal force fields, constant gradient chemotactic
field. Reported findings can be useful to get insights into very different
phenomena involving active particles, such as bacterial motion in external
fields, intracellular transport, cell migration, animal foraging
Holographic tracking and sizing of optically trapped microprobes in diamond anvil cells
We demonstrate that Digital Holographic Microscopy can be used for accurate 3D tracking and sizing of a colloidal probe trapped in a diamond anvil cell (DAC). Polystyrene beads were optically trapped in water up to Gigapascal pressures while simultaneously recording in-line holograms at 1 KHz frame rate. Using Lorenz-Mie scattering theory to fit interference patterns, we detected a 10% shrinking in the bead’s radius due to the high applied pressure. Accurate bead sizing is crucial for obtaining reliable viscosity measurements and provides a convenient optical tool for the determination of the bulk modulus of probe material. Our technique may provide a new method for pressure measurements inside a DAC
Signal integration enhances the dynamic range in neuronal systems
The dynamic range measures the capacity of a system to discriminate the
intensity of an external stimulus. Such an ability is fundamental for living
beings to survive: to leverage resources and to avoid danger. Consequently, the
larger is the dynamic range, the greater is the probability of survival. We
investigate how the integration of different input signals affects the dynamic
range, and in general the collective behavior of a network of excitable units.
By means of numerical simulations and a mean-field approach, we explore the
nonequilibrium phase transition in the presence of integration. We show that
the firing rate in random and scale-free networks undergoes a discontinuous
phase transition depending on both the integration time and the density of
integrator units. Moreover, in the presence of external stimuli, we find that a
system of excitable integrator units operating in a bistable regime largely
enhances its dynamic range.Comment: 5 pages, 4 figure
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