Model inspired by population genetics to study fragmentation of brittle plates

We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence of (i) composite scaling laws, (ii) small critical exponents \tau associated with the power-law fragment-size distribution, and (iii) the typical pattern of cracks. The proposed computer simulations do not require numerical solutions of the Newton's equations of motion, nor several additional assumptions normally used in discrete element models. The model is also able to predict some physical aspects which could be tested in new experiments of fragmentation of brittle systems.Comment: We have modified the text in order to make the description of the model more clear. One Figure (Figure 1) was introduced showing the steps of the dynamics of colonization. Twelve references were adde

Conservation law for distributed entanglement of formation and quantum discord

We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey a conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.Comment: Published versio

Overcoming ambiguities in classical and quantum correlation measures

We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discordlike quantifiers. More specifically, we determine situations for which either classical or quantum correlations are not uniquely defined due to degeneracies arising from the optimization procedure over the state space. In order to remove such degeneracies, we introduce a general approach where correlations are independently defined, escaping therefore from a degenerate subspace. As an illustration, we analyze the trace-norm geometric quantum discord for two-qubit Bell-diagonal states.Comment: 5 pages, 2 figures. v2: Minor corrections. Published versio

Inclusive hadron and photon production at LHC in dipole momentum space

Using a momentum space model for the dipole scattering amplitude we present an analysis of the saturation effects at LHC energies, describing the data on proton-proton and proton-lead collisions. The model is based on the asymptotic solutions of the Balitsky-Kovchegov equation, being ideal in the saturation domain where the target wave function has a high occupation number. We also make predictions for the nuclear modification ratios on charged hadron and prompt photon production in the forward region, where the high parton density effects are important.Comment: New section added and typos corrected. To be published in PR

Sunflower yield: adjustement of data means by the combination of ANOVA and Regression models.

Sunflower is an important oilseed crop. Besides producing high quality edible oil for human consumption, it also produces meal for animal feeding, and is an alternative for biodiesel production as well. Sunflower is a crop well adapted to several environmental conditions and is tolerant to low temperatures and to relatively short periods of water stress. In Brazil, the sunflower cultivated area reaches 75,000 hectares and its yield averages 1,460 kg/ha (CONAB). Much effort has been spent on research work at management of sunflower and consequently higher yield. Research efforts are specifically directed to the control of diseases and pests, which can cause defoliation, damages to the roots, and yield losses. The need for macro- and micronutrient fertilizations is another research demanding aspect of the crop. Within this context, two extremely important aspects in solving these research demands are: the appropriate agronomical planning and the adequate experimental design. These procedures will allow decisions on selection of size and shape of plots, on experimental unit, on qualitative and quantitative factors, on experimental design, and on the choice of the variables that influence the response and the ways of choosing and distributing the treatments in the plots. The selection of the suitable statistical methods, which allow precise estimates of the treatments and the reduction of the residual variance, uncontrolled in the planning, is also essential. One of these methods is the Analysis of Covariance (ANCOVA). This method combines the Analysis of Variance (ANOVA) and the Regression Analysis, and besides controlling the experimental error, it adjusts the treatment means, thus helping the interpretation of the experimental results as well as the comparison of regressions among several groups of treatments. The model representing this combination is :Yij = ? + ? i + ? j + ? (xij - x.. ) +? ij , where: Yij is the observed value of the response variable; ? is the mean value of the response variable; i ? is the effect of treatment I, with i = 1, 2,?, I; j ? is the effect of the block j, with j = 1,2,?, J; ? is the effect of the combined linear regression Yij as related to x; ij x is the observed value of the co-variable; and ij ? is the experimental error associated toYij, with ?ij ?N (0,?2 ) . The covariate should not be influenced by the treatments initially tested, maintaining the independence among them. Therefore, the treatments were: one control (0), and the P2O5 dosages of 40 kg ha-1, 80 kg ha-1, 120 kg ha-1, and 160 kg ha-1, applied to the sunflower hybrid Aguara 4. The experiment was carried out as a randomized block design, with six replications and the variables studied were: yield (kg ha-1) and the number of achenes per sunflower plant. The descriptive analysis indicated consistency in the tests concerning normality and independence of errors, additivity of the model, and homogeneity of treatments variances. The F statistics presented significant response for the treatments, for the response variable and covariate (5.48 and 4.93), respectively. The highest sunflower yield, obtained with the dosage of 120 kg ha-1 P2O5, statistically differed only from the control (Tukey p? 0, 05). The ANCOVA, adjusted by the number of achenes, reduced the error variance from 49,768.84 to 32,887.40. An interesting fact is that after ANCOVA, the effect of treatments became non-significant (F = 2.62), even with the reduction of the error variance. The mean values adjusted by the Tukey-Kramer test were reduced when compared to the original means. The interaction of treatment with the covariable was not significant, indicating that the angular coefficients for the treatments were similar. We concluded that the analysis of covariance reduces the error variance and indicates the real significance of the treatment effects and of the angular coefficients for the non-homogeneous treatments

Unintegrated parton distributions in nuclei

We study how unintegrated parton distributions in nuclei can be calculated from the corresponding integrated partons using the EPS09 parametrization. The role of nuclear effects is presented in terms of the ratio $R^A=\text{uPDF}^A/A\cdot \text{PDF}^N$ for both large and small $x$ domains.Comment: 9 pages, 4 figure

Physical properties of the Schur complement of local covariance matrices

General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state $\rho_{12}$ described by a $4\times 4$ covariance matrix \textbf{V}, the Schur complement of a local covariance submatrix $\textbf{V}_1$ of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. The connection with a partial parity measurement over a bipartite quantum state and the determination of the reduced Wigner function is given and an operational process of parity measurement is developed. Generalization of this procedure to a $n$-partite Gaussian state is given and it is demonstrated that the $n-1$ system state conditioned to a partial parity projection is given by a covariance matrix such as its $2 \times 2$ block elements are Schur complements of special local matrices.Comment: 10 pages. Replaced with final published versio

Geometric classical and total correlations via trace distance

We introduce the concepts of geometric classical and total correlations through Schatten 1-norm (trace norm), which is the only Schatten p-norm able to ensure a well-defined geometric measure of correlations. In particular, we derive the analytical expressions for the case of two-qubit Bell-diagonal states, discussing the superadditivity of geometric correlations. As an illustration, we compare our results with the entropic correlations, discussing both their hierarchy and monotonicity properties. Moreover, we apply the geometric correlations to investigate the ground state of spin chains in the thermodynamic limit. In contrast to the entropic quantifiers, we show that the classical correlation is the only source of 1-norm geometric correlation that is able to signaling an infinite-order quantum phase transition.Comment: v2: published versio