Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics

The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to be encountered in this system was done by examining the stability of the steady state in linear response as well as constructing a two-parameter phase diagram in the ($a -\omega$) plane. Numerical explorations revealed varieties of bifurcation sequences including quasiperiodic route to chaos. Besides, the familiar period-doubling and crises route to chaos exhibited by the one-dimensional ratchet were also found. In addition, the coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of bifurcations. Chaotic behaviour is characterized by using the sensitivity to initial condition as well as the Lyapunov exponent spectrum; while a perusal of the phase space projected in the Poincar$\acute{e}$ cross-section confirms some of the striking features.Comment: 7 pages; 8 figure

Constant Approximation for kk-Median and kk-Means with Outliers via Iterative Rounding

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon the large implicit constant approximation ratio of Chen [Chen, SODA 2018]. For $k$-means with outliers, we give an $(\alpha_2+\epsilon \leq 53.002 + \epsilon)$-approximation, which is the first $O(1)$-approximation for this problem. The iterative algorithm framework is very versatile; we show how it can be used to give $\alpha_1$- and $(\alpha_1 + \epsilon)$-approximation algorithms for matroid and knapsack median problems respectively, improving upon the previous best approximations ratios of $8$ [Swamy, ACM Trans. Algorithms] and $17.46$ [Byrka et al, ESA 2015]. The natural LP relaxation for the $k$-median/$k$-means with outliers problem has an unbounded integrality gap. In spite of this negative result, our iterative rounding framework shows that we can round an LP solution to an almost-integral solution of small cost, in which we have at most two fractionally open facilities. Thus, the LP integrality gap arises due to the gap between almost-integral and fully-integral solutions. Then, using a pre-processing procedure, we show how to convert an almost-integral solution to a fully-integral solution losing only a constant-factor in the approximation ratio. By further using a sparsification technique, the additive factor loss incurred by the conversion can be reduced to any $\epsilon > 0$

The transcriptomic evolution of mammalian pregnancy:gene expression innovations in endometrial stromal fibroblasts

The endometrial stromal fibroblast (ESF) is a cell type present in the uterine lining of therian mammals. In the stem lineage of eutherian mammals, ESF acquired the ability to differentiate into decidual cells in order to allow embryo implantation. We call the latter cell type “neo-ESF” in contrast to “paleo-ESF” which is homologous to eutherian ESF but is not able to decidualize. In this study, we compare the transcriptomes of ESF from six therian species: Opossum (Monodelphis domestica; paleo-ESF), mink, rat, rabbit, human (all neo-ESF), and cow (secondarily nondecidualizing neo-ESF). We find evidence for strong stabilizing selection on transcriptome composition suggesting that the expression of approximately 5,600 genes is maintained by natural selection. The evolution of neo-ESF from paleo-ESF involved the following gene expression changes: Loss of expression of genes related to inflammation and immune response, lower expression of genes opposing tissue invasion, increased markers for proliferation as well as the recruitment of FOXM1, a key gene transiently expressed during decidualization. Signaling pathways also evolve rapidly and continue to evolve within eutherian lineages. In the bovine lineage, where invasiveness and decidualization were secondarily lost, we see a re-expression of genes found in opossum, most prominently WISP2, and a loss of gene expression related to angiogenesis. The data from this and previous studies support a scenario, where the proinflammatory paleo-ESF was reprogrammed to express anti-inflammatory genes in response to the inflammatory stimulus coming from the implanting conceptus and thus paving the way for extended, trans-cyclic gestation

SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22,380 nodes using 671,400 threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains simulation input file

Conduction of Ultracold Fermions Through a Mesoscopic Channel

In a mesoscopic conductor electric resistance is detected even if the device is defect-free. We engineer and study a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induce a current through the channel and find ohmic conduction, even for a ballistic channel. An analysis of in-situ density distributions shows that in the ballistic case the chemical potential drop occurs at the entrance and exit of the channel, revealing the presence of contact resistance. In contrast, a diffusive channel with disorder displays a chemical potential drop spread over the whole channel. Our approach opens the way towards quantum simulation of mesoscopic devices with quantum gases

Simulating combined SO2 and CO2 capture from combustion flue gas

The requirement to pre‐treat flue gas prior to the CO2 capture step is an economic challenge when using aqueous amine absorbents for capturing CO2 from coal‐fired power station flue gases. A potentially lower cost alternative is to combine the capture of both CO2 and SO2 from the flue gas into a single process, removing the requirement for the desulfurization pre‐treatment step. The CSIRO's CS‐Cap process uses a single aqueous amine absorbent to capture both of these acid gases from flue gas streams. This paper covers the initial simulation of this process applied to both brown and black coal flue gases. Removal of absorbed SO2 is achieved via reactive crystallization. This is simulated here using a ‘black box’ process, resulting in a K2SO4 product. Different operating conditions have been evaluated that increase the sulfate concentration of the absorbent in the SO2 capture section of the process, which is expected to increase the efficiency of the reactive crystallization step. This paper provides information on the absorption of SO2 into the amine solution, and heat and mass balances for the wider process. This information will be required for further detailed simulation of the reactive crystallization step, and economic evaluation of the CS‐Cap process. © 2019 Society of Chemical Industry and John Wiley & Sons, Ltd

Impact of Microstructure of Nanoscale Magnetron Sputtered Ru/Al Multilayers on Thermally Induced Phase Formation

In this study, we report on phase formation and microstructure evolution in multiscale magnetron sputtered Ru/Al multilayers upon thermal annealing in vacuum at slow heating rates of 10 K/min. By specifically adjusting the microstructure and design of the as-deposited multilayers, the formation of certain desired phases can be tuned. We demonstrate that the synthesis of single phase RuAl thin films is possible in a very controlled manner in a solid state only via thermal activation without initiating the self-propagating exothermic reactions of Ru/Al multilayers. To investigate phase formation sequences and the resulting microstructures, Ru/Al multilayers were designed via magnetron sputtering with systematic variation of bilayer modulation periods and subsequent vacuum annealing. Thin films samples were characterized by in situ high-temperature XRD, TEM imaging and diffraction. It is shown that different phase sequences appear in strong correlation with the modulation length. Depending on the multilayer design, the phase formation toward single-phase RuAl thin films happens as either a multi-step or single-step event. In particular, below a critical threshold of the modulation period, the multi-step phase formation can be suppressed, and only the desired RuAl target phase is obtained with a pronounced growth in a preferred orientation. This finding may be versatile for the targeted synthesis of intermetallic phases, contributing to further understanding of phase formation in such nanoscale multilayer systems

Impact of Microstructure of Nanoscale Magnetron Sputtered Ru/Al Multilayers on Thermally Induced Phase Formation

In this study, we report on phase formation and microstructure evolution in multiscale magnetron sputtered Ru/Al multilayers upon thermal annealing in vacuum at slow heating rates of 10 K/min. By specifically adjusting the microstructure and design of the as-deposited multilayers, the formation of certain desired phases can be tuned. We demonstrate that the synthesis of single phase RuAl thin films is possible in a very controlled manner in a solid state only via thermal activation without initiating the self-propagating exothermic reactions of Ru/Al multilayers. To investigate phase formation sequences and the resulting microstructures, Ru/Al multilayers were designed via magnetron sputtering with systematic variation of bilayer modulation periods and subsequent vacuum annealing. Thin films samples were characterized by in situ high-temperature XRD, TEM imaging and diffraction. It is shown that different phase sequences appear in strong correlation with the modulation length. Depending on the multilayer design, the phase formation toward single-phase RuAl thin films happens as either a multi-step or single-step event. In particular, below a critical threshold of the modulation period, the multi-step phase formation can be suppressed, and only the desired RuAl target phase is obtained with a pronounced growth in a preferred orientation. This finding may be versatile for the targeted synthesis of intermetallic phases, contributing to further understanding of phase formation in such nanoscale multilayer systems