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 $\bar{\rho^q(r)}$ of the local order parameter $\rho(r)$ scale with a set $x(q)$ of non-trivial exponents $x(q) \neq q x(1)$. In this paper, we revisit these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w(r)$ normalized over space $\sum_r w(r)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder averaged values of the generalized moments $Y_q =\sum_r w^q(r)$, since they may scale with different generalized dimensions $D(q)$ and $\tilde D(q)$ (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 $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths ordered clusters at criticality determines the asymptotic value $x(q \to \infty) =d$ and the minimal value $\alpha_{min}=D(q \to \infty)=d-x(1)$ of the typical multifractal spectrum $f(\alpha)$.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