1,043 research outputs found
Conformal approach to cylindrical DLA
We extend the conformal mapping approach elaborated for the radial Diffusion
Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in
particular a complex function which allows to grow a cylindrical cluster using
as intermediate step a radial aggregate. The grown aggregate exhibits the same
self-affine features of the original cylindrical DLA. The specific choice of
the transformation allows us to study the relationship between the radial and
the cylindrical geometry. In particular the cylindrical aggregate can be seen
as a radial aggregate with particles of size increasing with the radius. On the
other hand the radial aggregate can be seen as a cylindrical aggregate with
particles of size decreasing with the height. This framework, which shifts the
point of view from the geometry to the size of the particles, can open the way
to more quantitative studies on the relationship between radial and cylindrical
DLA.Comment: 16 pages, 8 figure
Analysis of patterns formed by two-component diffusion limited aggregation
We consider diffusion limited aggregation of particles of two different
kinds. It is assumed that a particle of one kind may adhere only to another
particle of the same kind. The particles aggregate on a linear substrate which
consists of periodically or randomly placed particles of different kinds. We
analyze the influence of initial patterns on the structure of growing clusters.
It is shown that at small distances from the substrate, the cluster structures
repeat initial patterns. However, starting from a critical distance the initial
periodicity is abruptly lost, and the particle distribution tends to a random
one. An approach describing the evolution of the number of branches is
proposed. Our calculations show that the initial patter can be detected only at
the distance which is not larger than approximately one and a half of the
characteristic pattern size.Comment: Accepted for publication in Physical Review
Multifractal Dimensions for Branched Growth
A recently proposed theory for diffusion-limited aggregation (DLA), which
models this system as a random branched growth process, is reviewed. Like DLA,
this process is stochastic, and ensemble averaging is needed in order to define
multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys.
Rev. A46, 7793 (1992)], annealed average dimensions were computed for this
model. In this paper, we compute the quenched average dimensions, which are
expected to apply to typical members of the ensemble. We develop a perturbative
expansion for the average of the logarithm of the multifractal partition
function; the leading and sub-leading divergent terms in this expansion are
then resummed to all orders. The result is that in the limit where the number
of particles n -> \infty, the quenched and annealed dimensions are {\it
identical}; however, the attainment of this limit requires enormous values of
n. At smaller, more realistic values of n, the apparent quenched dimensions
differ from the annealed dimensions. We interpret these results to mean that
while multifractality as an ensemble property of random branched growth (and
hence of DLA) is quite robust, it subtly fails for typical members of the
ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl
Exact Multifractal Exponents for Two-Dimensional Percolation
The harmonic measure (or diffusion field or electrostatic potential) near a
percolation cluster in two dimensions is considered. Its moments, summed over
the accessible external hull, exhibit a multifractal spectrum, which I
calculate exactly. The generalized dimensions D(n) as well as the MF function
f(alpha) are derived from generalized conformal invariance, and are shown to be
identical to those of the harmonic measure on 2D random walks or self-avoiding
walks. An exact application to the anomalous impedance of a rough percolative
electrode is given. The numerical checks are excellent. Another set of exact
and universal multifractal exponents is obtained for n independent
self-avoiding walks anchored at the boundary of a percolation cluster. These
exponents describe the multifractal scaling behavior of the average nth moment
of the probabity for a SAW to escape from the random fractal boundary of a
percolation cluster in two dimensions.Comment: 5 pages, 3 figures (in colors
Gradient-limited surfaces
A simple scenario of the formation of geological landscapes is suggested and
the respective lattice model is derived. Numerical analysis shows that the
arising non-Gaussian surfaces are characterized by the scale-dependent Hurst
exponent, which varies from 0.7 to 1, in agreement with experimental data.Comment: 4 pages, 5 figure
Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface
We study the dynamics of a system of hard-core particles sliding downwards on
a one dimensional fluctuating interface, which in a special case can be mapped
to the problem of a passive scalar advected by a Burgers fluid. Driven by the
surface fluctuations, the particles show a tendency to cluster, but the
hard-core interaction prevents collapse. We use numerical simulations to
measure the auto-correlation function in steady state and in the aging regime,
and space-time correlation functions in steady state. We have also calculated
these quantities analytically in a related surface model. The steady state
auto-correlation is a scaling function of t/L^z, where L is the system size and
z the dynamic exponent. Starting from a finite intercept, the scaling function
decays with a cusp, in the small argument limit. The finite value of the
intercept indicates the existence of long range order in the system. The
space-time correlation, which is a function of r/L and t/L^z, is non-monotonic
in t for fixed r. The aging auto-correlation is a scaling function of t_1 and
t_2 where t_1 is the waiting time and t_2 the time difference. This scaling
function decays as a power law for t_2 \gg t_1; for t_1 \gg t_2, it decays with
a cusp as in steady state. To reconcile the occurrence of strong fluctuations
in the steady state with the fact of an ordered state, we measured the
distribution function of the length of the largest cluster. This shows that
fluctuations never destroy ordering, but rather the system meanders from one
ordered configuration to another on a relatively rapid time scale
On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
Disordered systems present multifractal properties at criticality. In
particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639
(1990)) on the case of diluted two-dimensional Potts model, the moments
of the local order parameter scale with a set
of non-trivial exponents . In this paper, we revisit
these ideas to incorporate more recent findings: (i) whenever a multifractal
measure normalized over space occurs in a random
system, it is crucial to distinguish between the typical values and the
disorder averaged values of the generalized moments , since
they may scale with different generalized dimensions and
(ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E
{\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces
a lack of self-averaging at critical points for thermodynamic observables, in
particular for the order parameter. After this general discussion valid for any
random critical point, we apply these ideas to random polymer models that can
be studied numerically for large sizes and good statistics over the samples. We
study the bidimensional wetting or the Poland-Scheraga DNA model with loop
exponent (marginal disorder) and (relevant disorder). Finally,
we argue that the presence of finite Griffiths ordered clusters at criticality
determines the asymptotic value and the minimal value of the typical multifractal spectrum
.Comment: 17 pages, 20 figure
The effect of self-affine fractal roughness of wires on atom chips
Atom chips use current flowing in lithographically patterned wires to produce
microscopic magnetic traps for atoms. The density distribution of a trapped
cold atom cloud reveals disorder in the trapping potential, which results from
meandering current flow in the wire. Roughness in the edges of the wire is
usually the main cause of this behaviour. Here, we point out that the edges of
microfabricated wires normally exhibit self-affine roughness. We investigate
the consequences of this for disorder in atom traps. In particular, we consider
how closely the trap can approach the wire when there is a maximum allowable
strength of the disorder. We comment on the role of roughness in future
atom--surface interaction experiments.Comment: 7 pages, 7 figure
DNA transfer in forensic science: A review
© 2018 Elsevier B.V. Understanding the variables impacting DNA transfer, persistence, prevalence and recovery (DNA-TPPR) has become increasingly relevant in investigations of criminal activities to provide opinion on how the DNA of a person of interest became present within the sample collected. This review considers our current knowledge regarding DNA-TPPR to assist casework investigations of criminal activities. There is a growing amount of information available on DNA-TPPR to inform the relative probabilities of the evidence given alternative scenarios relating to the presence or absence of DNA from a specific person in a collected sample of interest. This information should be used where relevant. However, far more research is still required to better understand the variables impacting DNA-TPPR and to generate more accurate probability estimates of generating particular types of profiles in more casework relevant situations. This review explores means of achieving this. It also notes the need for all those interacting with an item of interest to have an awareness of DNA transfer possibilities post criminal activity, to limit the risk of contamination or loss of DNA. Appropriately trained forensic practitioners are best placed to provide opinion and guidance on the interpretation of profiles at the activity level. However, those requested to provide expert opinion on DNA-related activity level issues are often insufficiently trained to do so. We advocate recognition of DNA activity associated expertise to be distinct from expertise associated with the identification of individuals. This is to be supported by dedicated training, competency testing, authorisation, and regular fit for purpose proficiency testing. The possibilities for experts to report on activity-related issues will increase as our knowledge increases through further research, access to relevant data is enhanced, and tools to assist interpretations are better exploited. Improvement opportunities will be achieved sooner, if more laboratories and agencies accept the need to invest in these aspects as well as the training of practitioners
DNA Transfer in Forensic Science: Recent Progress towards Meeting Challenges.
Understanding the factors that may impact the transfer, persistence, prevalence and recovery of DNA (DNA-TPPR), and the availability of data to assign probabilities to DNA quantities and profile types being obtained given particular scenarios and circumstances, is paramount when performing, and giving guidance on, evaluations of DNA findings given activity level propositions (activity level evaluations). In late 2018 and early 2019, three major reviews were published on aspects of DNA-TPPR, with each advocating the need for further research and other actions to support the conduct of DNA-related activity level evaluations. Here, we look at how challenges are being met, primarily by providing a synopsis of DNA-TPPR-related articles published since the conduct of these reviews and briefly exploring some of the actions taken by industry stakeholders towards addressing identified gaps. Much has been carried out in recent years, and efforts continue, to meet the challenges to continually improve the capacity of forensic experts to provide the guidance sought by the judiciary with respect to the transfer of DNA
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