28,112 research outputs found
A Fractional Lie Group Method For Anomalous Diffusion Equations
Lie group method provides an efficient tool to solve a differential equation.
This paper suggests a fractional partner for fractional partial differential
equations using a fractional characteristic method. A space-time fractional
diffusion equation is used as an example to illustrate the effectiveness of the
Lie group method.Comment: 5 pages,in pres
Variational Iteration Method for q
Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness
Enhancing quantum entropy in vacuum-based quantum random number generator
Information-theoretically provable unique true random numbers, which cannot
be correlated or controlled by an attacker, can be generated based on quantum
measurement of vacuum state and universal-hashing randomness extraction.
Quantum entropy in the measurements decides the quality and security of the
random number generator. At the same time, it directly determine the extraction
ratio of true randomness from the raw data, in other words, it affects quantum
random numbers generating rate obviously. In this work, considering the effects
of classical noise, the best way to enhance quantum entropy in the vacuum-based
quantum random number generator is explored in the optimum dynamical
analog-digital converter (ADC) range scenario. The influence of classical noise
excursion, which may be intrinsic to a system or deliberately induced by an
eavesdropper, on the quantum entropy is derived. We propose enhancing local
oscillator intensity rather than electrical gain for noise-independent
amplification of quadrature fluctuation of vacuum state. Abundant quantum
entropy is extractable from the raw data even when classical noise excursion is
large. Experimentally, an extraction ratio of true randomness of 85.3% is
achieved by finite enhancement of the local oscillator power when classical
noise excursions of the raw data is obvious.Comment: 12 pages,8 figure
A New Two-Dimensional Functional Material with Desirable Bandgap and Ultrahigh Carrier Mobility
Two-dimensional (2D) semiconductors with direct and modest bandgap and
ultrahigh carrier mobility are highly desired functional materials for
nanoelectronic applications. Herein, we predict that monolayer CaP3 is a new 2D
functional material that possesses not only a direct bandgap of 1.15 eV (based
on HSE06 computation), and also a very high electron mobility up to 19930 cm2
V-1 s-1, comparable to that of monolayer phosphorene. More remarkably, contrary
to the bilayer phosphorene which possesses dramatically reduced carrier
mobility compared to its monolayer counterpart, CaP3 bilayer possesses even
higher electron mobility (22380 cm2 V-1 s-1) than its monolayer counterpart.
The bandgap of 2D CaP3 can be tuned over a wide range from 1.15 to 0.37 eV
(HSE06 values) through controlling the number of stacked CaP3 layers. Besides
novel electronic properties, 2D CaP3 also exhibits optical absorption over the
entire visible-light range. The combined novel electronic, charge mobility, and
optical properties render 2D CaP3 an exciting functional material for future
nanoelectronic and optoelectronic applications
Lie group classifications and exact solutions for time-fractional Burgers equation
Lie group method provides an efficient tool to solve nonlinear partial
differential equations. This paper suggests a fractional Lie group method for
fractional partial differential equations. A time-fractional Burgers equation
is used as an example to illustrate the effectiveness of the Lie group method
and some classes of exact solutions are obtained.Comment: 9 pp, accepte
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