518 research outputs found
Noise-induced phase transitions: Effects of the noises' statistics and spectrum
The local, uncorrelated multiplicative noises driving a second-order, purely
noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and
white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The
potential scientific and technological interest of this phenomenon calls for a
study of the effects of the noises' statistics and spectrum. This task is
facilitated if these noises are dynamically generated by means of stochastic
differential equations (SDE) driven by white noises. One such case is that of
Ornstein--Uhlenbeck noises which are stationary, with Gaussian pdf and a
variance reduced by the self-correlation time (\tau), and whose effect on the
NIPT phase diagram has been studied some time ago. Another such case is when
the stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a
\emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for
(q<1), allows for a controlled exploration of the effects of the departure from
Gaussian statistics. As done before with stochastic resonance and other
phenomena, we now exploit this tool to study--within a simple mean-field
approximation and with an emphasis on the \emph{order parameter} and the
``\emph{susceptibility}''--the combined effect on NIPT of the noises'
statistics and spectrum. Even for relatively small (\tau), it is shown that
whereas fat-tail noise distributions ((q>1)) counteract the effect of
self-correlation, compact-support ones ((q<1)) enhance it. Also, an interesting
effect on the susceptibility is seen in the last case.Comment: 6 pages, 10 figures, uses aipproc.cls, aip-8s.clo and aipxfm.sty. To
appear in AIP Conference Proceedings. Invited talk at MEDYFINOL'06 (XV
Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics
Invited review: KPZ. Recent developments via a variational formulation
Recently, a variational approach has been introduced for the paradigmatic
Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together
with the functional Taylor expansion that the KPZ nonequilibrium potential
(NEP) admits. Such expansion becomes naturally truncated at third order, giving
rise to a nonlinear stochastic partial differential equation to be regarded as
a gradient-flow counterpart to the KPZ equation. A dynamic renormalization
group analysis at one-loop order of this new mesoscopic model yields the KPZ
scaling relation alpha+z=2, as a consequence of the exact cancelation of the
different contributions to vertex renormalization. This result is quite
remarkable, considering the lower degree of symmetry of this equation, which is
in particular not Galilean invariant. In addition, this scheme is exploited to
inquire about the dynamical behavior of the KPZ equation through a
path-integral approach. Each of these aspects offers novel points of view and
sheds light on particular aspects of the dynamics of the KPZ equation.Comment: 16 pages, 2 figure
Analisis Pengaruh Hari Perdagangan terhadap Abnormal Return Saham LQ-45 yang Terdaftar di Bursa Efek Indonesia
Penelitian ini bertujuan untuk menganalisis day of the week effect menggunakan 37 Perusahaan yang terdaftar di indeks LQ 45 Bursa Efek Indonesia periode Februari 2012 hingga Januari 2013 sebagai sampel, dan tujuan berikutnya dalam penelitian ini adalah untuk menganalisis apakah Perubahan pada abnormal return hari Jumat mempengaruhi Perubahan return hari Senin minggu berikutnya. Penelitian ini menggunakan model GARCH untuk tujuan pertama dan OLS untuk tujuan kedua. Hasil empiris menunjukkan abnormal return negatif terendah pada hari Senin dan return positif tertinggi pada hari Jumat, keduanya signifikan secara statistik pada tingkat 10%. Return positif tertinggi kedua terjadi pada hari Kamis dan secara statistik pada tingkat 5%. Berdasarkan hasil penelitian tersebut, sebaiknya investor menahan atau membeli saham pada hari Senin dan menjual saham pada hari Kamis atau hari Jumat. Lebih lanjut lagi tidak ada bukti yang signifikan terkait return hari Senin digerakkan oleh abnormal return hari Jumat minggu sebelumnya sehingga abnormal return hari Jumat minggu sebelumnya sebaiknya tidak digunakan dalam memperkirakan return pada hari Senin minggu berikutnya
Algorithms for Colourful Simplicial Depth and Medians in the Plane
The colourful simplicial depth of a point x in the plane relative to a
configuration of n points in k colour classes is exactly the number of closed
simplices (triangles) with vertices from 3 different colour classes that
contain x in their convex hull. We consider the problems of efficiently
computing the colourful simplicial depth of a point x, and of finding a point,
called a median, that maximizes colourful simplicial depth.
For computing the colourful simplicial depth of x, our algorithm runs in time
O(n log(n) + k n) in general, and O(kn) if the points are sorted around x. For
finding the colourful median, we get a time of O(n^4). For comparison, the
running times of the best known algorithm for the monochrome version of these
problems are O(n log(n)) in general, improving to O(n) if the points are sorted
around x for monochrome depth, and O(n^4) for finding a monochrome median.Comment: 17 pages, 8 figure
Structure of Fermionic Density Matrices: Complete N-representability Conditions
We present a constructive solution to the N-representability problem---a full
characterization of the conditions for constraining the two-electron reduced
density matrix (2-RDM) to represent an N-electron density matrix. Previously
known conditions, while rigorous, were incomplete. Here we derive a hierarchy
of constraints built upon (i) the bipolar theorem and (ii) tensor
decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2,
known classical conditions, and new conditions appear naturally. Subsets of the
conditions are amenable to polynomial-time computations of strongly correlated
systems
Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
In order to perform numerical simulations of the KPZ equation, in any
dimensionality, a spatial discretization scheme must be prescribed. The known
fact that the KPZ equation can be obtained as a result of a Hopf--Cole
transformation applied to a diffusion equation (with \emph{multiplicative}
noise) is shown here to strongly restrict the arbitrariness in the choice of
spatial discretization schemes. On one hand, the discretization prescriptions
for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen.
On the other hand, since the discretization is an operation performed on
\emph{space} and the Hopf--Cole transformation is \emph{local} both in space
and time, the former should be the same regardless of the field to which it is
applied. It is shown that whereas some discretization schemes pass both
consistency tests, known examples in the literature do not. The requirement of
consistency for the discretization of Lyapunov functionals is argued to be a
natural and safe starting point in choosing spatial discretization schemes. We
also analyze the relation between real-space and pseudo-spectral discrete
representations. In addition we discuss the relevance of the Galilean
invariance violation in these consistent discretization schemes, and the
alleged conflict of standard discretization with the fluctuation--dissipation
theorem, peculiar of 1D.Comment: RevTex, 23pgs, 2 figures, submitted to Phys. Rev.
Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability
We recently presented a constructive solution to the N-representability
problem of the two-electron reduced density matrix (2-RDM)---a systematic
approach to constructing complete conditions to ensure that the 2-RDM
represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev.
Lett. 108, 263002 (2012)]. In this paper we provide additional details and
derive further N-representability conditions on the 2-RDM that follow from the
constructive solution. The resulting conditions can be classified into a
hierarchy of constraints, known as the (2,q)-positivity conditions where the q
indicates their derivation from the nonnegativity of q-body operators. In
addition to the known T1 and T2 conditions, we derive a new class of
(2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity
conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of
(2,6)-positivity conditions. The constraints obtained can be divided into two
general types: (i) lifting conditions, that is conditions which arise from
lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity
conditions and (ii) pure conditions, that is conditions which cannot be derived
from a simple lifting of the lower conditions. All of the lifting conditions
and the pure (2,q)-positivity conditions for q>3 require tensor decompositions
of the coefficients in the model Hamiltonians. Subsets of the new
N-representability conditions can be employed with the previously known
conditions to achieve polynomially scaling calculations of ground-state
energies and 2-RDMs of many-electron quantum systems even in the presence of
strong electron correlation
An update on the Hirsch conjecture
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to
George Dantzig. It states that the graph of a d-dimensional polytope with n
facets cannot have diameter greater than n - d.
Despite being one of the most fundamental, basic and old problems in polytope
theory, what we know is quite scarce. Most notably, no polynomial upper bound
is known for the diameters that are conjectured to be linear. In contrast, very
few polytopes are known where the bound is attained. This paper collects
known results and remarks both on the positive and on the negative side of the
conjecture. Some proofs are included, but only those that we hope are
accessible to a general mathematical audience without introducing too many
technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2
and put into the appendix arXiv:0912.423
Perbandingan Metode Uji Kandungan Total Fenolik Dari Ekstrak Rumput Laut Eucheuma Cottonii Lontar Banten
Rumput laut adalah suatu komoditas utama perikanan budidaya di Indonesia yang menopang hampir 58% dari total produksi perikanan budidaya tahun 2016 yang mencapai 19,46 juta ton. Salah satu rumput laut yaitu rumput laut E. Cottoni diketahui memiliki kandungan senyawa fenolik yang merupakan salah satu kandungan rumput laut yang berperan sebagai antioksidan. Rumput laut Eucheuma Cottonii terdapat senyawa flavonoid seperti catechin (gallocathecin, epicathecin, catechin gallate), flavonols, flavonol glycosides, caffeic acid, hesperidin, myricetin yang berfungsi sebagai antioksidan. Tujuan mengetahui metode ekstraksi terbaik dalam uji kandungan fenolik dalam rumput laut (Euchema cotonii) dan menentukan konsentrasi optimal pada pelarut (metanol) dalam proses ekstraksi rumput laut (Euchema cotonii). Penelitin ini dilakukan dengan cara mengekstraksi kandungan rumput laut dengan berbagai metode ekstraksi yaitu maserasi, ultrasonic dan microwave dengan konsentrasi pelarut etanol (25% ;50% ;75%) lalu dilakukan pengukuran kadar total fenolik dengan metode folin ciocalteau dan dianalisa absorbansinya dengan spectrophotometer UV-Vis. Hasil Total Phenolic Compound (TPC) terbaik dalam penelitian ini yakni pada metode ekstraksi ultrasonik dan dengan pelarut etanol pada konsentrasi 50% yakni sebesar 961.081 mg GAE / g ekstra
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