Stochastic kinetic theory applied to coarse-grained polymer model

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from the full field theory. The accuracy of the field theory and moment equations are quantified using autocorrelation functions. The full field theory is only accurate for large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points

Systematic development of coarse-grained polymer models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2006.Includes bibliographical references (p. [159]-163).The coupling between polymer models and experiments has improved our understanding of polymer behavior both in terms of rheology and dynamics of single molecules. Developing these polymer models is challenging because of the wide range of time and length scales. Mechanical models of polymers have been used to understand average heological properties as well as the deviation a single polymer molecule has from the average response. This leads to more physically significant constitutive relations, which can be coupled with fluid mechanic simulations to predict and understand the theological response of polymer solutions and melts. These models have also been used in conjunction with single molecule polymer experiments. While these have provided insight into the dynamics of polymers in rheological flows, they have also helped to design single molecule manipulation experiments. Promising research in this area includes DNA separation and stretching devices. A typical atomic bond has a length of 10-10m and vibration time scale of 10-14s. A typical experiment in a microfluidic device has lengths of order 10-5m and times of order 102s. It is not possible to capture these larger length and time scales of interest while capturing exactly the behavior at the smaller length and time scales.(cont.) This necessitates a process of coarse-graining which sacrifices the details at the small scale which are not necessary while retaining the important features that do affect the response at the larger scales. This thesis focuses on the coarse-graining of polymers into a series of beads connected by springs. The function which gives the retractive force in the spring as a function of the extension is called the spring force law. In many new microfluidic applications the previously used spring force laws produce significant errors in the model. We have systematically analyzed the coarse-graining and development of the spring force law to understand why these force laws fail. In particular, we analyzed the force-extension behavior which quantifies how much the polymer extends under application of an external force. We identified the key dimensionless group that governs the response and found that it is important to understand the different constraints under which the polymer is placed. This understanding led to the development of new spring force laws which are accurate coarse-grained models by construction. We also examined the response in other situations such as weak and strong flows.(cont.) This further illustrated the disadvantages of the previous force laws which were eliminated by using the new force laws. This thesis will have practical impact because the new spring force laws can easily be implemented in current polymer models. This will improve the accuracy of the models and place the models on firmer theoretical footing. Because the spring force law has been developed independently of other coarse-grained interactions, this thesis will also help in determining the best parameters for other interactions because they will not need to compensate for an error in the spring force law. These new spring force laws will help form the framework of coarse-grained models which can help understand a wide range of situations in which the behavior at a small scale affects the large time and length scale behavior.by Patrick Theodore Underhill.Ph.D

Effect of viscoelasticity on the collective behavior of swimming microorganisms

Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. Using a mean-field theory and the Oldroyd-B constitutive equation, we show how linear viscoelasticity of the suspending fluid alters the hydrodynamic interactions and therefore the ability of the group to coordinate. We quantify the ability to coordinate by the initial growth rate of a small disturbance from the uniform isotropic state. For small wave numbers the response is qualitatively similar to a Newtonian fluid but the Deborah number affects an effective viscosity of the suspension. At higher wave number, the response of the fluid to small amplitude oscillatory shear flow, leads to a maximal growth rate at a particular wavelength unlike the Newtonian result

Diffusion and spatial correlations in suspensions of swimming particles

Populations of swimming microorganisms produce fluid motions that lead to dramatically enhanced diffusion of tracer particles. Using simulations of suspensions of swimming particles in a periodic domain, we capture this effect and show that it depends qualitatively on the mode of swimming: swimmers ``pushed'' from behind by their flagella show greater enhancement than swimmers that are ``pulled'' from the front. The difference is manifested by an increase, that only occurs for pushers, of the diffusivity of passive tracers and the velocity correlation length with the size of the periodic domain. A physical argument supported by a mean field theory sheds light on the origin of these effects.Comment: 10 pages, 3 figures, to be published in Phys. Rev. Let

Rare isotope production in statistical multifragmentation

Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble. Both the initial fragmentation and the the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments. The importance of sequential decay, exact particle-number conservation and the sensitivities to parameters such as density and temperature are explored. Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture.Comment: 10 eps figure

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Comparative genomic and phylogeographic analysis of Mycobacterium leprae

Reductive evolution and massive pseudogene formation have shaped the 3.31-Mb genome of Mycobacterium leprae, an unculturable obligate pathogen that causes leprosy in humans. The complete genome sequence of M. leprae strain Br4923 from Brazil was obtained by conventional methods (6 x coverage), and Illumina resequencing technology was used to obtain the sequences of strains Thai53 (38 x coverage) and NHDP63 (46 x coverage) from Thailand and the United States, respectively. Whole-genome comparisons with the previously sequenced TN strain from India revealed that the four strains share 99.995% sequence identity and differ only in 215 polymorphic sites, mainly SNPs, and by 5 pseudogenes. Sixteen interrelated SNP subtypes were defined by genotyping both extant and extinct strains of M. leprae from around the world. The 16 SNP subtypes showed a strong geographical association that reflects the migration patterns of early humans and trade routes, with the Silk Road linking Europe to China having contributed to the spread of leprosy