39,568 research outputs found
Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF)
collocation approach to solve the Volterra's model for population growth of a
species within a closed system. This model is a nonlinear integro-differential
equation where the integral term represents the effect of toxin. This approach
is based on orthogonal functions which will be defined. The collocation method
reduces the solution of this problem to the solution of a system of algebraic
equations. We also compare these methods with some other numerical results and
show that the present approach is applicable for solving nonlinear
integro-differential equations.Comment: 18 pages, 5 figures; Published online in the journal of "Mathematical
Methods in the Applied Sciences
Topological phase in one-dimensional interacting fermion system
We study a one-dimensional interacting topological model by means of exact
diagonalization method. The topological properties are firstly examined with
the existence of the edge states at half-filling. We find that the topological
phases are not only robust to small repulsive interactions but also are
stabilized by small attractive interactions, and also finite repulsive
interaction can drive a topological non-trivial phase into a trivial one while
the attractive interaction can drive a trivial phase into a non-trivial one.
Next we calculate the Berry phase and parity of the bulk system and find that
they are equivalent in characterizing the topological phases. With them we
obtain the critical interaction strengths and construct part of the phase
diagram in the parameters space. Finally we discuss the effective Hamiltonian
at large-U limit and provide additional understanding of the numerical results.
Our these results could be realized experimentally using cold atoms trapped in
the 1D optical lattice.Comment: 7 pages, 5 figures; revised version, references added, Accepted for
publication in Physical Review
Optimal Monetary Policy Rules in A Simple Stochastic Macro Model: China's Evidence
In this paper we apply a simple macro model to explore and evaluate certain optimal monetary policy rules for China's economy. To be more consistent with the central bank (the People's Bank of China)'s behaviour, we use money supply as a monetary policy instrument rather than the commonly used interest rate. Policy rules are optimal in terms of minimizing the predetermined loss functions, and the parameters of these rules are determined by stochastic simulation. Different forms of policy rule and loss function are considered, especially for exchange rate volatility and money supply volatility. The optimality of monetary policy rules is evaluated by comparing the shifts of policy frontiers.Monetary Policy Rule, Loss Function, Stochastic Simulation, Policy Frontier, China
An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method
Based on a new approximation method, namely pseudospectral method, a solution
for the three order nonlinear ordinary differential laminar boundary layer
Falkner-Skan equation has been obtained on the semi-infinite domain. The
proposed approach is equipped by the orthogonal Hermite functions that have
perfect properties to achieve this goal. This method solves the problem on the
semi-infinite domain without truncating it to a finite domain and transforming
domain of the problem to a finite domain. In addition, this method reduces
solution of the problem to solution of a system of algebraic equations. We also
present the comparison of this work with numerical results and show that the
present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of
"Communications in Nonlinear Science and Numerical Simulation
Dynamic hydration valve controlled ion permeability and stability of NaK channel
The K^+^, Na^+^, Ca^2+^ channels are essential to neural signalling, but our current knowledge at atomic level is mainly limited to that of K^+^ channels. Unlike a K^+^ channel having four equivalent K^+^-binding sites in its selectivity filter, a NaK channel conducting both Na^+^ and K^+^ ions has a vestibule in the middle part of its selectivity filter, in which ions can diffuse but not bind specifically. However, how the NaK channel conducts ions remains elusive. Here we find four water grottos connecting with the vestibule of the NaK selectivity filter. Molecular dynamics and free energy calculations show that water molecules moving in the vestibule-grotto complex hydrate and stabilize ions in the filter and serve as a valve in conveying ions through the vestibule for controllable ion permeating. During ion conducting, the water molecules are confined within the valve to guarantee structure stability. The efficient exquisite hydration valve should exist and play similar roles in the large family of cyclic nucleotide-gated channels which have similar selectivity filter sequences. The exquisite hydration valve mechanism may shed new light on the importance of water in neural signalling
Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field
The thermal entanglement in a two-spin-qutrit system with two spins coupled
by exchange interaction under a magnetic field in an arbitrary direction is
investigated. Negativity, the measurement of entanglement, is calculated. We
find that for any temperature the evolvement of negativity is symmetric with
respect to magnetic field. The behavior of negativity is presented for four
different cases. The results show that for different temperature, different
magnetic field give maximum entanglement. Both the parallel and antiparallel
magnetic field cases are investigated qualitatively (not quantitatively) in
detail, we find that the entanglement may be enhanced under an antiparallel
magnetic field.Comment: 2 eps figure
Efficient Approximation Algorithms for Multi-Antennae Largest Weight Data Retrieval
In a mobile network, wireless data broadcast over channels (frequencies)
is a powerful means for distributed dissemination of data to clients who access
the channels through multi-antennae equipped on their mobile devices. The
-antennae largest weight data retrieval (ALWDR) problem is to
compute a schedule for downloading a subset of data items that has a maximum
total weight using antennae in a given time interval. In this paper,
we propose a ratio approximation algorithm for the
-antennae largest weight data retrieval (ALWDR) problem that
has the same ratio as the known result but a significantly improved time
complexity of from
when
\cite{lu2014data}. To our knowledge, our algorithm represents the first ratio
approximation solution to ALWDR for the
general case of arbitrary . To achieve this, we first give a ratio
algorithm for the -separated ALWDR
(ALWDR) with runtime , under the assumption
that every data item appears at most once in each segment of
ALWDR, for any input of maximum length on channels in
time slots. Then, we show that we can retain the same ratio for
ALWDR without this assumption at the cost of increased time
complexity to . This result immediately yields an
approximation solution of same ratio and time complexity for ALWDR,
presenting a significant improvement of the known time complexity of ratio
approximation to the problem
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