844,574 research outputs found

### The hard-disk fluid revisited

The hard-disk model plays a role of touchstone for testing and developing the
transport theory. By large scale molecular dynamics simulations of this model,
three important autocorrelation functions, and as a result the corresponding
transport coefficients, i.e., the diffusion constant, the thermal conductivity
and the shear viscosity, are found to deviate significantly from the
predictions of the conventional transport theory beyond the dilute limit. To
improve the theory, we consider both the kinetic process and the hydrodynamic
process in the whole time range, rather than each process in a seperated time
scale as the conventional transport theory does. With this consideration, a
unified and coherent expression free of any fitting parameters is derived
succesfully in the case of the velocity autocorrelation function, and its
superiority to the conventional `piecewise' formula is shown. This expression
applies to the whole time range and up to moderate densities, and thus bridges
the kinetics and hydrodynamics approaches in a self-consistent manner.Comment: 5 pages, 4 figure

### Brownian motion: from kinetics to hydrodynamics

Brownian motion has served as a pilot of studies in diffusion and other
transport phenomena for over a century. The foundation of Brownian motion, laid
by Einstein, has generally been accepted to be far from being complete since
the late 1960s, because it fails to take important hydrodynamic effects into
account. The hydrodynamic effects yield a time dependence of the diffusion
coefficient, and this extends the ordinary hydrodynamics. However, the time
profile of the diffusion coefficient across the kinetic and hydrodynamic
regions is still absent, which prohibits a complete description of Brownian
motion in the entire course of time. Here we close this gap. We manage to
separate the diffusion process into two parts: a kinetic process governed by
the kinetics based on molecular chaos approximation and a hydrodynamics process
described by linear hydrodynamics. We find the analytical solution of vortex
backflow of hydrodynamic modes triggered by a tagged particle. Coupling it to
the kinetic process we obtain explicit expressions of the velocity
autocorrelation function and the time profile of diffusion coefficient. This
leads to an accurate account of both kinetic and hydrodynamic effects. Our
theory is applicable for fluid and Brownian particles, even of irregular-shaped
objects, in very general environments ranging from dilute gases to dense
liquids. The analytical results are in excellent agreement with numerical
experiments.Comment: 8pages,3figure

### Modified Stokes-Einstein Relation for Small Brownian Particles

The Stokes-Einstein (SE) relation has been widely applied to quantitatively
describe the Brownian motion. Notwithstanding, here we show that even for a
simple fluid, the SE relation may not be completely applicable. Namely,
although the SE relation could be a good approximation for a large enough
Brownian particle, we find that it induces significant error for a smaller
Brownian particle, and the error increases with the decrease of the Brownian
particle's size, till the SE relation fails completely when the size of
Brownian particle is comparable with that of a fluid molecule. The cause is
rooted in the fact that the kinetic and the hydrodynamic effects depend on the
size of the Brownian particle differently. By excluding the kinetic
contribution to the diffusion coefficient, we propose a revised Stokes-Einstein
relation and show that it expands significantly the applicable range.Comment: 3 figure

### NormalNet: Learning-based Normal Filtering for Mesh Denoising

Mesh denoising is a critical technology in geometry processing that aims to
recover high-fidelity 3D mesh models of objects from their noise-corrupted
versions. In this work, we propose a learning-based normal filtering scheme for
mesh denoising called NormalNet, which maps the guided normal filtering (GNF)
into a deep network. The scheme follows the iterative framework of
filtering-based mesh denoising. During each iteration, first, the voxelization
strategy is applied on each face in a mesh to transform the irregular local
structure into the regular volumetric representation, therefore, both the
structure and face normal information are preserved and the convolution
operations in CNN(Convolutional Neural Network) can be easily performed.
Second, instead of the guidance normal generation and the guided filtering in
GNF, a deep CNN is designed, which takes the volumetric representation as
input, and outputs the learned filtered normals. At last, the vertex positions
are updated according to the filtered normals. Specifically, the iterative
training framework is proposed, in which the generation of training data and
the network training are alternately performed, whereas the ground truth
normals are taken as the guidance normals in GNF to get the target normals.
Compared to state-of-the-art works, NormalNet can effectively remove noise
while preserving the original features and avoiding pseudo-features

### The 2-adic valuations of differences of Stirling numbers of the second kind

Let $m, n, k$ and $c$ be positive integers. Let $\nu_2(k)$ be the 2-adic
valuation of $k$. By $S(n,k)$ we denote the Stirling numbers of the second
kind. In this paper, we first establish a convolution identity of the Stirling
numbers of the second kind and provide a detailed 2-adic analysis to the
Stirling numbers of the second kind. Consequently, we show that if $2\le m\le
n$ and $c$ is odd, then $\nu_2(S(c2^{n+1},2^m-1)-S(c2^n, 2^m-1))=n+1$ except
when $n=m=2$ and $c=1$, in which case $\nu_2(S(8,3)-S(4,3))=6$. This solves a
conjecture of Lengyel proposed in 2009.Comment: 20 page

### Divisibility by 2 of Stirling numbers of the second kind and their differences

Let $n,k,a$ and $c$ be positive integers and $b$ be a nonnegative integer.
Let $\nu_2(k)$ and $s_2(k)$ be the 2-adic valuation of $k$ and the sum of
binary digits of $k$, respectively. Let $S(n,k)$ be the Stirling number of the
second kind. It is shown that $\nu_2(S(c2^n,b2^{n+1}+a))\geq s_2(a)-1,$ where
$0<a<2^{n+1}$ and $2\nmid c$. Furthermore, one gets that
$\nu_2(S(c2^{n},(c-1)2^{n}+a))=s_2(a)-1$, where $n\geq 2$, $1\leq a\leq 2^n$
and $2\nmid c$. Finally, it is proved that if $3\leq k\leq 2^n$ and $k$ is not
a power of 2 minus 1, then
$\nu_2(S(a2^{n},k)-S(b2^{n},k))=n+\nu_2(a-b)-\lceil\log_2k\rceil
+s_2(k)+\delta(k),$ where $\delta(4)=2$, $\delta(k)=1$ if $k>4$ is a power of
2, and $\delta(k)=0$ otherwise. This confirms a conjecture of Lengyel raised in
2009 except when $k$ is a power of 2 minus 1.Comment: 23 pages. To appear in Journal of Number Theor

### An Algorithm of Parking Planning for Smart Parking System

There are so many vehicles in the world and the number of vehicles is
increasing rapidly. To alleviate the parking problems caused by that, the smart
parking system has been developed. The parking planning is one of the most
important parts of it. An effective parking planning strategy makes the better
use of parking resources possible. In this paper, we present a feasible method
to do parking planning. We transform the parking planning problem into a kind
of linear assignment problem. We take vehicles as jobs and parking spaces as
agents. We take distances between vehicles and parking spaces as costs for
agents doing jobs. Then we design an algorithm for this particular assignment
problem and solve the parking planning problem. The method proposed can give
timely and efficient guide information to vehicles for a real time smart
parking system. Finally, we show the effectiveness of the method with
experiments over some data, which can simulate the situation of doing parking
planning in the real world.Comment: Proceeding of the 11th World Congress on Intelligent Control and
Automation (WCICA

### The 2-adic valuations of Stirling numbers of the second kind

In this paper, we investigate the 2-adic valuations of the Stirling numbers
$S(n, k)$ of the second kind. We show that $v_2(S(4i, 5))=v_2(S(4i+3, 5))$ if
and only if $i\not\equiv 7\pmod {32}$. This confirms a conjecture of
Amdeberhan, Manna and Moll raised in 2008. We show also that $v_2(S(2^n+1,
k+1))= s_2(n)-1$ for any positive integer $n$, where $s_2(n)$ is the sum of
binary digits of $n$. It proves another conjecture of Amdeberhan, Manna and
Moll.Comment: 9 pages. To appear in International Journal of Number Theor

### The universal Kummer congruences

Let $p$ be a prime. In this paper, we present a detailed $p$-adic analysis to
factorials and double factorials and their congruences. We give good bounds for
the $p$-adic sizes of the coefficients of the divided universal Bernoulli
number ${{\hat B_n}\over n}$ when $n$ is divisible by $p-1$. Using these we
then establish the universal Kummer congruences modulo powers of a prime $p$
for the divided universal Bernoulli numbers ${{\hat B_n}\over n}$ when $n$ is
divisible by $p-1$.Comment: 20 pages. To appear in Journal of the Australian Mathematical Societ

### Classification of entities via their descriptive sentences

Hypernym identification of open-domain entities is crucial for taxonomy
construction as well as many higher-level applications. Current methods suffer
from either low precision or low recall. To decrease the difficulty of this
problem, we adopt a classification-based method. We pre-define a concept
taxonomy and classify an entity to one of its leaf concept, based on the name
and description information of the entity. A convolutional neural network
classifier and a K-means clustering module are adopted for classification. We
applied this system to 2.1 million Baidu Baike entities, and 1.1 million of
them were successfully identified with a precision of 99.36%

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