8,892 research outputs found
The Primary Pretenders
We call a composite number q such that there exists a positive integer b with
b^p == b (mod q) a prime pretender to base b. The least prime pretender to base
b is the primary pretender q_b. It is shown that there are only 132 distinct
primary pretenders, and that q_b is a periodic function of b whose period is
the 122-digit number
19568584333460072587245340037736278982017213829337604336734362-
294738647777395483196097971852999259921329236506842360439300.Comment: 7 page
Determination of the critical current density in the d-wave superconductor YBCO under applied magnetic fields by nodal tunneling
We have studied nodal tunneling into YBa2Cu3O7-x (YBCO) films under magnetic
fields. The films' orientation was such that the CuO2 planes were perpendicular
to the surface with the a and b axis at 450 form the normal. The magnetic field
was applied parallel to the surface and perpendicular to the CuO2 planes. The
Zero Bias Conductance Peak (ZBCP) characteristic of nodal tunneling splits
under the effect of surface currents produced by the applied fields. Measuring
this splitting under different field conditions, zero field cooled and field
cooled, reveals that these currents have different origins. By comparing the
field cooled ZBCP splitting to that taken in decreasing fields we deduce a
value of the Bean critical current superfluid velocity, and calculate a Bean
critical current density of up to 3*10^7 A/cm2 at low temperatures. This
tunneling method for the determination of critical currents under magnetic
fields has serious advantages over the conventional one, as it avoids having to
make high current contacts to the sample.Comment: 8 pages, 2 figure
Fractional processes: from Poisson to branching one
Fractional generalizations of the Poisson process and branching Furry process
are considered. The link between characteristics of the processes, fractional
differential equations and Levy stable densities are discussed and used for
construction of the Monte Carlo algorithm for simulation of random waiting
times in fractional processes. Numerical calculations are performed and limit
distributions of the normalized variable Z=N/ are found for both processes.Comment: 11 pages, 6 figure
Proof without Words: On Sums of Squares and Triangles
author's final draft post-referee and pre-publication copySummary. We visually display a relationship between sums of squares and the sum of an even number of triangular numbers. Connections to some proofs without words appearing in the literature are briefly discussed.Ye
Structural characteristics of positionally-disordered lattices: relation to the first sharp diffraction peak in glasses
Positional disorder has been introduced into the atomic structure of certain
crystalline lattices, and the orientationally-averaged structure factor S(k)
and pair-correlation function g(r) of these disordered lattices have been
studied. Analytical expressions for S(k) and g(r) for Gaussian positional
disorder in 2D and 3D are confirmed with precise numerical simulations. These
analytic results also have a bearing on the unsolved Gauss circle problem in
mathematics. As the positional disorder increases, high-k peaks in S(k) are
destroyed first, eventually leaving a single peak, that with the lowest-k
value. The pair-correlation function for lattices with such high levels of
positional disorder exhibits damped oscillations, with a period equal to the
separation between the furthest-separated (lowest-k) lattice planes. The last
surviving peak in S(k) is, for example for silicon and silica, at a wavevector
nearly identical to that of the experimentally-observed first sharp diffraction
peak (FSDP) in the amorphous phases of those materials. Thus, for these
amorphous materials at least, the FSDP can be regarded as arising from
scattering from atomic configurations equivalent to the single family of
positionally-disordered local Bragg planes having the furthest separation.Comment: v2: changes in response to referees' comments: Figure 2 made more
readable, improved discussion of height of peaks in S(k), other minor changes
4 pages, 3 figures, submitted to Physical Review
Number theoretic example of scale-free topology inducing self-organized criticality
In this work we present a general mechanism by which simple dynamics running
on networks become self-organized critical for scale free topologies. We
illustrate this mechanism with a simple arithmetic model of division between
integers, the division model. This is the simplest self-organized critical
model advanced so far, and in this sense it may help to elucidate the mechanism
of self-organization to criticality. Its simplicity allows analytical
tractability, characterizing several scaling relations. Furthermore, its
mathematical nature brings about interesting connections between statistical
physics and number theoretical concepts. We show how this model can be
understood as a self-organized stochastic process embedded on a network, where
the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres
Type 1 adenylyl cyclase is essential for maintenance of remote contextual fear memory
Although molecular mechanisms for hippocampus-dependent memory have been extensively studied, much less is known about signaling events important for remote memory. Here we report that mice lacking type 1 adenylyl cyclase (AC1) are able to establish and retrieve remote contextual memory but unable to sustain it as long as wild-type mice. Interestingly, mice overexpressing AC1 show superior remote contextual memory even though they exhibit normal hippocampus-dependent contextual memory. These data illustrate that calcium coupling to cAMP contributes to the stability of remote memory and identifies AC1 as a potential drug target site to improve long-term remote memory
Quantum circuits with uniformly controlled one-qubit gates
Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some
result
Competitiveness and sustainability: can ‘smart city regionalism’ square the circle?
Increasingly, the widely established, globalisation-driven agenda of economic competitiveness meets a growing concern with sustainability. Yet, the practical and conceptual co-existence—or fusion—of these two agendas is not always easy. This includes finding and operationalising the ‘right’ scale of governance, an important question for the pursuit of the distinctly transscalar nature of these two policy fields. ‘New regionalism’ has increasingly been discussed as a pragmatic way of tackling the variable spatialities associated with these policy fields and their changing articulation. This paper introduces ‘smart (new) city-regionalism’, derived from the principles of smart growth and new regionalism, as a policy-shaping mechanism and analytical framework. It brings together the rationales, agreed principles and legitimacies of publicly negotiated polity with collaborative, network-based and policy-driven spatiality. The notion of ‘smartness’, as suggested here as central feature, goes beyond the implicit meaning of ‘smart’ as in ‘smart growth’. When introduced in the later 1990s the term embraced a focus on planning and transport. Since then, the adjective ‘smart’ has become used ever more widely, advocating innovativeness, participation, collaboration and co-ordination. The resulting ‘smart city regionalism’ is circumscribed by the interface between the sectorality and territoriality of policy-making processes. Using the examples of Vancouver and Seattle, the paper looks at the effects of the resulting specific local conditions on adopting ‘smartness’ in the scalar positioning of policy-making
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