Mapping the phase diagram of strongly interacting matter

We employ a conformal mapping to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$. This method allows us to identify the singularity corresponding to the critical point of a second-order phase transition at finite $\mu$, given information only at $\mu=0$. The scheme is potentially useful for computing thermodynamic properties of strongly interacting hot and dense matter in lattice gauge theory. The technique is illustrated by an application to a chiral effective model.Comment: 5 pages, 3 figures; published versio

Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.

Transforming NMR spectroscopy : extraction of multiplet parameters with deep learning

Accurate extraction of multiplet parameters, such as J-couplings and chemical shifts, play a vital role in small molecule analysis using nuclear magnetic resonance (NMR) spectroscopy. These parameters provide essential quantitative information about molecular structures, interatomic interactions, and chemical environments, enabling precise characterization of small organic compounds. This poster presents an innovative omputational approach that utilizes state-of-the-art deep learning techniques, specifically detection transformers, to automate and optimize the extraction of multiplet parameters from 1D NMR spectra of small molecules. By incorporating these advanced computational methods, experimenters can achieve improved efficiency, accuracy, and speed in analyzing and characterizing small organic compounds using NMR spectroscopy

Deconvolution of NMR spectra : a deep learning-based approach

We introduce a deep learning-based deconvolution approach for 1H NMR spectra, developed by leveraging concepts from the field of physics informed-learning, intelligent labeling, and tailored high dynamic range (HDR) spectral preprocessing. Since automation and faster workflows are major concerns in NMR spectroscopy, the algorithm handles uncorrected spectra without strict assumptions on phase and baseline correction as well as line shape. Due to the lack of high quality and consistently labeled experimental spectra in quantities needed to train modern deep learning models, we relied on synthetic spectra creation. Moreover, instead of training with synthetic spectra consisting of single lines, we created synthetic multiples that further supported a realistic deconvolution. We achieved super-human performance on corrected and uncorrected synthetic spectra. Finally, and most importantly, the results on synthetic data translate well to experimental spectra despite the covariate shift. Thus, this tool is a promising candidate for automated expert-level deconvolution of experimental HDR 1H NMR spectra

On critical behaviour in systems of Hamiltonian partial differential equations

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\ue9-I (PI) equation or its fourth-order analogue P2I. As concrete examples, we discuss nonlinear Schr\uf6dinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture