Lamellae Stability in Confined Systems with Gravity

The microphase separation of a diblock copolymer melt confined by hard walls and in the presence of a gravitational field is simulated by means of a cell dynamical system model. It is found that the presence of hard walls normal to the gravitational field are key ingredients to the formation of well ordered lamellae in BCP melts. To this effect the currents in the directions normal and parallel to the field are calculated along the interface of a lamellar domain, showing that the formation of lamellae parallel to the hard boundaries and normal to the field correspond to the stable configuration. Also, it is found thet the field increases the interface width.Comment: 4 pages, 2 figures, submitted to Physical Review

Spinodal Decomposition and the Tomita Sum Rule

The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good agreement with numerical results for the order parameter scaling function in three dimensions. The values of the associated nonequilibrium decay exponents are given by the known lower bounds.Comment: 15 pages, 6 figure

Coalitions in International Litigation: A Network Perspective

We apply network science principles to analyze the coalitions formed by European Union (EU) nations and institutions during litigation proceedings at the European Court of Justice. By constructing Friends and Foes networks, we explore their characteristics and dynamics through the application of cluster detection, motif analysis, and duplex analysis. Our findings demonstrate that the Friends and Foes networks exhibit disassortative behavior, highlighting the inclination of nodes to connect with dissimilar nodes. Furthermore, there is a correlation among centrality measures, indicating that member states and institutions with a larger number of connections play a prominent role in bridging the network. An examination of the modularity of the networks reveals that coalitions tend to align along regional and institutional lines, rather than national government divisions. Additionally, an analysis of triadic binary motifs uncovers a greater level of reciprocity within the Foes network compared to the Friends network.Comment: 13 pages 11 figures, style and bibtex files include

Enhancing Transport Efficiency by Hybrid Routing Strategy

Traffic is essential for many dynamic processes on real networks, such as internet and urban traffic systems. The transport efficiency of the traffic system can be improved by taking full advantage of the resources in the system. In this paper, we propose a dual-strategy routing model for network traffic system, to realize the plenary utility of the whole network. The packets are delivered according to different "efficient routing strategies" [Yan, et al, Phys. Rev. E 73, 046108 (2006)]. We introduce the accumulate rate of packets, {\eta} to measure the performance of traffic system in the congested phase, and propose the so-called equivalent generation rate of packet to analyze the jamming processes. From analytical and numerical results, we find that, for suitable selection of strategies, the dual- strategy system performs better than the single-strategy system in a broad region of strategy mixing ratio. The analytical solution to the jamming processes is verified by estimating the number of jammed nodes, which coincides well with the result from simulation.Comment: 6 pages, 3 figure

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Calibrating the dice loss to handle neural network overconfidence for biomedical image segmentation

The Dice similarity coefficient (DSC) is both a widely used metric and loss function for biomedical image segmentation due to its robustness to class imbalance. However, it is well known that the DSC loss is poorly calibrated, resulting in overconfident predictions that cannot be usefully interpreted in biomedical and clinical practice. Performance is often the only metric used to evaluate segmentations produced by deep neural networks, and calibration is often neglected. However, calibration is important for translation into biomedical and clinical practice, providing crucial contextual information to model predictions for interpretation by scientists and clinicians. In this study, we provide a simple yet effective extension of the DSC loss, named the DSC++ loss, that selectively modulates the penalty associated with overconfident, incorrect predictions. As a standalone loss function, the DSC++ loss achieves significantly improved calibration over the conventional DSC loss across six well-validated open-source biomedical imaging datasets, including both 2D binary and 3D multi-class segmentation tasks. Similarly, we observe significantly improved calibration when integrating the DSC++ loss into four DSC-based loss functions. Finally, we use softmax thresholding to illustrate that well calibrated outputs enable tailoring of recall-precision bias, which is an important post-processing technique to adapt the model predictions to suit the biomedical or clinical task. The DSC++ loss overcomes the major limitation of the DSC loss, providing a suitable loss function for training deep learning segmentation models for use in biomedical and clinical practice. Source code is available at https://github.com/mlyg/DicePlusPlus

Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as $R = [B \tau]^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(\delta t,\bar{t})$, where $\delta t = k^{1/n} B |\tau_2-\tau_1|$ and $\bar{t} = k^{1/n} B (\tau_1+\tau_2)/2$. Both analytically and numerically, the covariance is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the small-$\bar{t}$ limit and $\delta t/\bar{t} ^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{\tau_1^{2n}+\tau_2^{2n}}),\tau_1/\tau_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $\lambda \approx 4.47$, violating an upper bound conjectured by Fisher and Huse.Comment: RevTex: 11 pages + 12 figures, submitted to PR

Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.Comment: To appear in PRE, figures available on reques

Measurement of Lagrangian velocity in fully developed turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR