36,053 research outputs found
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs
In this work we study a sequence of perfect t-embeddings of uniformly
weighted Aztec diamonds. We show that these perfect t-embeddings can be used to
prove convergence of gradients of height fluctuations to those of the Gaussian
free field. In particular we provide a first proof of the existence of a model
satisfying all conditions of the main theorem of arXiv:2109.06272. This
confirms the prediction of arXiv:2002.07540. An important part of our proof is
to exhibit exact integral formulas for perfect t-embeddings of uniformly
weighted Aztec diamonds.
In addition, we construct and analyze perfect t-embeddings of another
sequence of uniformly weighted finite graphs called tower graphs. Although we
do not check all technical assumptions of the mentioned theorem for these
graphs, we use perfect t-embeddings to derive a simple transformation which
identifies height fluctuations on the tower graph with those of the Aztec
diamond.Comment: 45 pages, 18 figures. v2: minor edits to introduction, fixed typo
Error Free Perfect Secrecy Systems
Shannon's fundamental bound for perfect secrecy says that the entropy of the
secret message cannot be larger than the entropy of the secret key initially
shared by the sender and the legitimate receiver. Massey gave an information
theoretic proof of this result, however this proof does not require
independence of the key and ciphertext. By further assuming independence, we
obtain a tighter lower bound, namely that the key entropy is not less than the
logarithm of the message sample size in any cipher achieving perfect secrecy,
even if the source distribution is fixed. The same bound also applies to the
entropy of the ciphertext. The bounds still hold if the secret message has been
compressed before encryption.
This paper also illustrates that the lower bound only gives the minimum size
of the pre-shared secret key. When a cipher system is used multiple times, this
is no longer a reasonable measure for the portion of key consumed in each
round. Instead, this paper proposes and justifies a new measure for key
consumption rate. The existence of a fundamental tradeoff between the expected
key consumption and the number of channel uses for conveying a ciphertext is
shown. Optimal and nearly optimal secure codes are designed.Comment: Submitted to the IEEE Trans. Info. Theor
Extended Aharonov-Bohm period analysis of strongly correlated electron systems
The `extended Aharonov-Bohm (AB) period' recently proposed by Kusakabe and
Aoki [J. Phys. Soc. Jpn (65), 2772 (1996)] is extensively studied numerically
for finite size systems of strongly correlated electrons. While the extended AB
period is the system length times the flux quantum for noninteracting systems,
we have found the existence of the boundary across which the period is halved
or another boundary into an even shorter period on the phase diagram for these
models. If we compare this result with the phase diagram predicted from the
Tomonaga-Luttinger theory, devised for low-energy physics, the halved period
(or shorter periods) has a one-to-one correspondence to the existence of the
pairing (phase separation or metal-insulator transition) in these models. We
have also found for the t-J model that the extended AB period does not change
across the integrable-nonintegrable boundary despite the totally different
level statistics.Comment: 26 pages, RevTex, 16 figures available on request from
[email protected], to be published in J. Phys. Soc. Jpn 66 No.
7(1997), We disscus the extended AB period of strongly correlated systems
more systematically by performing numerical calculation for the t-J-J' model
and the extended Hubbard model in addition to the 1D t-J model and the t-J
ladde
- …