343 research outputs found
Hyperbolic Schwarz map for the hypergeometric differential equation
The Schwarz map of the hypergeometric differential equation is studied since
the beginning of the last century. Its target is the complex projective line,
the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is
the hyperbolic 3-space. This map can be considered to be a lifting to the
3-space of the Schwarz map. This paper studies the singularities of this map,
and visualize its image when the monodromy group is a finite group or a typical
Fuchsian group. General cases will be treated in a forthcoming paper.Comment: 16 pages, 8 figure
Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts
In the previous paper (math.CA/0609196) we defined a map, called the
hyperbolic Schwarz map, from the one-dimensional projective space to the
three-dimensional hyperbolic space by use of solutions of the hypergeometric
differential equation, and thus obtained closed flat surfaces belonging to the
class of flat fronts. We continue the study of such flat fronts in this paper.
First, we introduce the notion of derived Schwarz maps of the hypergeometric
differential equation and, second, we construct a parallel family of flat
fronts connecting the classical Schwarz map and the derived Schwarz map.Comment: 15 pages, 12 figure
Quantum algorithm for collisionless Boltzmann simulation of self-gravitating systems
The collisionless Boltzmann equation (CBE) is a fundamental equation that
governs the dynamics of a broad range of astrophysical systems from space
plasma to star clusters and galaxies. It is computationally expensive to
integrate the CBE directly in a phase space, and thus the applications to
realistic astrophysical problems have been limited so far. Recently, Todorova
\& Steijl (2020) proposed an efficient quantum algorithm for solving the CBE
with a significantly reduced computational complexity. We extend the method to
perform quantum simulations that follow the evolution of self-gravitating
systems. We first run a 1+1 dimensional test calculation of free streaming
motion on 6464 grids using 13 simulated qubits and validate our method.
We then perform simulations of Jeans collapse, and compare the result with
analytic and linear theory calculations. We propose a direct method to generate
initial conditions as well as a method to retrieve necessary information from a
register of multiple qubits. Our simulation scheme achieves
less computational complexity than the classical method,
where is the number of discrete velocity grids per dimension. It will
thus allow us to perform large-scale CBE simulations on future quantum
computers.Comment: 10 pages, 9figure
Simultaneous Improvements in Performance and Durability of an Octahedral PtNix/C Electrocatalyst for Next-Generation Fuel Cells by Continuous, Compressive, and Concave Pt Skin Layers
Simultaneous improvements in oxygen reduction reaction (ORR) activity and long-term durability of Pt-based cathode catalysts are indispensable for the development of next-generation polymer electrolyte fuel cells but are still a major dilemma. We present a robust octahedral core–shell PtNix/C electrocatalyst with high ORR performance (mass activity and surface specific activity 6.8–16.9 and 20.3–24.0 times larger than those of Pt/C, respectively) and durability (negligible loss after 10000 accelerated durability test (ADT) cycles). The key factors of the robust octahedral nanostructure (core–shell Pt73Ni27/C) responsible for the remarkable activity and durability were found to be three continuous Pt skin layers with 2.0–3.6% compressive strain, concave facet arrangements (concave defects and high coordination), a symmetric Pt/Ni distribution, and a Pt67Ni33 intermetallic core, as found by STEM-EDS, in situ XAFS, XPS, etc. The robust core–shell Pt73Ni27/C was produced by the partial release of the stress, Pt/Ni rearrangement, and dimension reduction of an as-synthesized octahedral Pt50Ni50/C with 3.6–6.7% compressive Pt skin layers by Ni leaching during the activation process. The present results on the tailored synthesis of the PtNix structure and composition and the better control of the robust catalytic architecture renew the current knowledge and viewpoint for instability of octahedral PtNix/C samples to provide a new insight into the development of next-generation PEFC cathode catalysts
Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos
Miyamoto K., Yamazaki S., Uchida F., et al. Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos. Physical Review Research 6, 013200 (2024); https://doi.org/10.1103/PhysRevResearch.6.013200.Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and, conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the (6+1)-dimensional space and is thus computationally demanding: Configuring ngr grid points in each coordinate and nt time grid points leads to O(ngr6) memory space and O(ntngr6) queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase-space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy ϵ and query complexity of order Õ[(ngr+nt)/ϵ]. Our method also reduces the space complexity to O[polylog(ngr/ϵ)] in terms of the qubit number, while using quantum random access memories with O(ngr3) entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy
Equilibriums of extremely magnetized compact stars with force-free magnetotunnels
We present numerical solutions for stationary and axisymmetric equilibriums
of compact stars associated with extremely strong magnetic fields. The interior
of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD)
conditions, while in the region of negligible mass density the force-free
conditions or electromagnetic vacuum are assumed. Solving all components of
Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free
conditions, equilibriums of rotating compact stars associated with mixed
poloidal and toroidal magnetic fields are obtained. It is found that in the
extreme cases the strong mixed magnetic fields concentrating in a toroidal
region near the equatorial surface expel the matter and form a force-free
toroidal magnetotunnel. We also introduce a new differential rotation law for
computing solutions associated with force-free magnetosphere, and present other
extreme models without the magnetotunnel.Comment: 13 pages, 4 figure
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