Lieb's Theorem and Maximum Entropy Condensates

The maximum entropy steady states which form upon Floquet heating of the ground state of the Hubbard model on unbalanced bi-partite lattices are shown to possess uniform finite off-diagonal long-range order in the thermodynamic limit. For repulsive interactions the induced order corresponds to the formation of a spin-wave condensate, whilst for attractive interactions it instead corresponds to the formation of a superconducting, $\eta$-paired condensate. This creation of a `hot' condensate can occur on any periodically driven unbalanced lattice where the relevant SU(2) symmetry is preserved. Our results provide an understanding of how strong driving can expose order which has been suppressed by the lattice geometry - independent of any microscopic parameters. We discuss the implications of this for recent experiments observing emergent superconductivity in solid-state photoexcited compounds.Comment: 5 pages, 2 figures, comments are welcom

Theory of commensurable magnetic structures in holmium

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the tau=5/18 structure observed a few degrees below T_N in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.Comment: REVTEX, 31 pages, 7 postscript figure

Dynamical order and superconductivity in a frustrated many-body system

In triangular lattice structures, spatial anisotropy and frustration can lead to rich equilibrium phase diagrams with regions containing complex, highly entangled states of matter. In this work we study the driven two-rung triangular Hubbard model and evolve these states out of equilibrium, observing how the interplay between the driving and the initial state unexpectedly shuts down the particle-hole excitation pathway. This restriction, which symmetry arguments fail to predict, dictates the transient dynamics of the system, causing the available particle-hole degrees of freedom to manifest uniform long-range order. We discuss implications of our results for a recent experiment on photo-induced superconductivity in ${\rm \kappa - (BEDT-TTF)_{2}Cu[N(CN)_{2}]Br}$ molecules.Comment: Main Text: 7 Pages, 4 Figures, Supplementary: 4 Pages, 3 Figure

Electrical conduction by interface states in semiconductor heterojunctions

peer reviewedaudience: researcher, professionalElectrical conduction in semiconductor heterojunctions containing defect states in the interface region is studied. As the classical drift-diffusion mechanism cannot in any case explain electrical conduction in semiconductor heterojunctions, tunnelling involving interface states is often considered as a possible conduction path. A theoretical treatment is made where defect states in the interface region with a continuous energy distribution are included. Electrical conduction through this defect band then allows the transit of electrons from the conduction band of one semiconductor to the valence band of the second component. The analysis is initiated by electrical measurements on n-CdS/p-CdTe heterojunctions obtained by chemical vapour deposition of CdS on (111) oriented CdTe single crystals, for which current--voltage and capacitance--frequency results are shown. The theoretical analysis is based on the numerical resolution of Poisson's equation and the continuity equations of electrons, holes and defect states, where a current component corresponding to the defect band conduction is explicitly included. Comparison with the experimental curves shows that this formalism yields an efficient tool to model the conduction process through the interface region. It also allows us to determine critical values of the physical parameters when a particular step in the conduction mechanism becomes dominant

Characterization of growth and metabolism of the haloalkaliphile Natronomonas pharaonis

Natronomonas pharaonis is an archaeon adapted to two extreme conditions: high salt concentration and alkaline pH. It has become one of the model organisms for the study of extremophilic life. Here, we present a genome-scale, manually curated metabolic reconstruction for the microorganism. The reconstruction itself represents a knowledge base of the haloalkaliphile's metabolism and, as such, would greatly assist further investigations on archaeal pathways. In addition, we experimentally determined several parameters relevant to growth, including a characterization of the biomass composition and a quantification of carbon and oxygen consumption. Using the metabolic reconstruction and the experimental data, we formulated a constraints-based model which we used to analyze the behavior of the archaeon when grown on a single carbon source. Results of the analysis include the finding that Natronomonas pharaonis, when grown aerobically on acetate, uses a carbon to oxygen consumption ratio that is theoretically near-optimal with respect to growth and energy production. This supports the hypothesis that, under simple conditions, the microorganism optimizes its metabolism with respect to the two objectives. We also found that the archaeon has a very low carbon efficiency of only about 35%. This inefficiency is probably due to a very low P/O ratio as well as to the other difficulties posed by its extreme environment

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

Mathematics in Medical Diagnostics - 2022 Proceedings of the 4th International Conference on Trauma Surgery Technology

The 4th event of the Giessen International Conference Series on Trauma Surgery Technology took place on April, the 23rd 2022 in Warsaw, Poland. It aims to bring together practical application research, with a focus on medical imaging, and the TDA experts from Warsaw. This publication contains details of our presentations and discussions

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Cell killing and resistance in pre-operative breast cancer chemotherapy

<p>Abstract</p> <p>Background</p> <p>Despite the recent development of technologies giving detailed images of tumours <it>in vivo</it>, direct or indirect ways to measure how many cells are actually killed by a treatment or are resistant to it are still beyond our reach.</p> <p>Methods</p> <p>We designed a simple model of tumour progression during treatment, based on descriptions of the key phenomena of proliferation, quiescence, cell killing and resistance, and giving as output the macroscopically measurable tumour volume and growth fraction. The model was applied to a database of the time course of volumes of breast cancer in patients undergoing pre-operative chemotherapy, for which the initial estimate of proliferating cells by the measure of the percentage of Ki67-positive cells was available.</p> <p>Results</p> <p>The analysis recognises different patterns of response to treatment. In one subgroup of patients the fitting implied drug resistance. In another subgroup there was a shift to higher sensitivity during the therapy. In the subgroup of patients where killing of cycling cells had the highest score, the drugs showed variable efficacy against quiescent cells.</p> <p>Conclusion</p> <p>The approach was feasible, providing items of information not otherwise available. Additional data, particularly sequential Ki67 measures, could be added to the system, potentially reducing uncertainty in estimates of parameter values.</p

Expression of a prostate-associated protein, human glandular kallikrein (hK2), in breast tumours and in normal breast secretions

The recent demonstration of human glandular kallikrein (hK2) expression in a breast carcinoma cell line has suggested that this putatively prostate-restricted, steroid hormone-regulated protease may also be expressed in breast epithelium in vivo and secreted into the mammary duct system. Given that the only substrate yet identified for hK2 activity is the precursor of prostate-specific antigen (PSA), the expression of which in breast carcinomas may be associated with favourable prognosis, our purpose was to examine the expression pattern of both hK2 and PSA in breast tumour tissues. Cytosolic extracts of 336 primary breast carcinomas prepared for routine oestrogen receptor (ER) and progesterone receptor (PR) analysis, as well as 31 nipple aspirates from six women with non-diseased mammary glands, were assayed for hK2 and PSA using immunofluorometric assays developed by the authors. In the tumour extracts, measurable hK2 and PSA concentrations were detected in 53% and 73% of cases respectively, and were positively correlated to each other (r = 0.59, P = 0.0001). Higher concentrations of PSA and hK2 were found in tumours expressing steroid hormone receptors (P = 0.0001 for PSA and P = 0.0001 for hK2, by Wilcoxon tests for both ER and PR), and both PSA (r = 0.25, P = 0.0001) and hK2 (r = 0.22, P = 0.0001) correlated directly with PR levels. A negative correlation between patient age and PSA (r = –0.12, P = 0.03) was also found. Both proteins were present in nipple aspirate fluid at relatively high concentrations which were positively correlated (r = 0.53, P = 0.002). The molecular weights of the immunoreactive species quantified by the hK2 and PSA assays were established by high-performance liquid chromatography (HPLC) and were consistent with the known molecular weights of hK2 and PSA. Together these data provide the first evidence, to our knowledge, that both malignant breast tissue and normal breast secretion contain measurable quantities of hK2, and that the degree of hK2 expression or secretion is directly proportional to the expression of PSA and steroid hormone receptors. hK2 expression may therefore be a marker of steroid hormone action in breast tissue. © 2000 Cancer Research Campaig