Efficient on the fly calculation of time correlation functions in computer simulations

Ramı́rez, Jorge; Sukumaran, Sathish K.; Vorselaars, Bart; Likhtman, Alexei E.

doi:10.1063/1.3491098

Cited by 153 publications

(162 citation statements)

References 12 publications

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“…In computer simulations, the most convenient way of evaluating the stress relaxation is by using the fluctuation-dissipation theorem [102,103]. For each mode ℓ, we have:…”

Section: Stress Tensor and Stress Relaxationmentioning

confidence: 99%

“…The stress relaxation function is obtained from the stress fluctuations by means of the fluctuation-dissipation theorem [102,103]. Considering polydispersity we have…”

Section: Slow Sticky Relaxation Modesmentioning

confidence: 99%

“…In order to evaluate correlation functions in simulations, we use a multiple-tau correlator algorithm proposed by Ramirez et al [103].…”

Section: Stress Tensor and Stress Relaxationmentioning

confidence: 99%

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Linear shear and nonlinear extensional rheology of unentangled supramolecular side-chain polymers

Cui

Boudara

Huang

et al. 2018

Journal of Rheology

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Supramolecular polymers are important within a wide range of applications including printing, adhesives, coatings, cosmetics, surgery and nano-fabrication. The possibility to tune polymer properties through the control of supramolecular associations makes these materials both versatile and powerful. Here, we present a systematic investigation of the linear shear rheology for a series of unentangled ethylhexyl acrylate based polymers for which the concentration of randomly distributed supramolecular side-groups are systematically varied. We perform a detailed investigation of the appplicability of Time Temperature Superposition (TTS) for our polymers; small amplitude oscillatory shear rheology is combined with stress relaxation experiments to identify the dynamic range over which TTS is a reasonable approximation. Moreover, we find that the "stickyRouse" model normally used to interpret the rheological response of supramolecular polymers fits our experimental data well in the terminal regime, but is less successful in the rubbery plateau regime. We propose some modifications to the "sticky-Rouse" model, which includes more realistic assumptions with regards to (i) the random placement of the stickers along the backbone, (ii) the contributions from dangling chain ends and (iii) the chain motion upon dissociation of a sticker and re-association with a new co-ordination which involves a finite sized "hop" of the chain. Our model provides an improved description of the plateau region. Finally, we measure the extensional rheological response of one of our supramolecular polymers. For the probed extensional flow rates, which are small compared to the characteristic rates of sticker dynamics, we expect a Rouse-type description to work well. We test this by modeling the observed strain hardening using the upper convected Maxwell model and demonstrate that this simple model can describe the data well, confirming the prediction and supporting our determination of sticker dynamics based on linear shear rheology. * k.j.l.mattsson@leeds.ac.uk 2

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“…In computer simulations, the most convenient way of evaluating the stress relaxation is by using the fluctuation-dissipation theorem [102,103]. For each mode ℓ, we have:…”

Section: Stress Tensor and Stress Relaxationmentioning

confidence: 99%

“…The stress relaxation function is obtained from the stress fluctuations by means of the fluctuation-dissipation theorem [102,103]. Considering polydispersity we have…”

Section: Slow Sticky Relaxation Modesmentioning

confidence: 99%

See 1 more Smart Citation

Linear shear and nonlinear extensional rheology of unentangled supramolecular side-chain polymers

Cui

Boudara

Huang

et al. 2018

Journal of Rheology

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“…For the shortest time span (n=0), up to p events the autocorrelation is directly calculated at the highest time resolution. The auto correlation at a lag time j, of a collection of events fi can be written as 3

F_{j} = \frac{1}{N - J} true \sum_{i = 0}^{N - j - 1} f_{i} f_{i + j},

Where the subscript j indicates single point on the spectrum of possible the time differences between discrete events that is of interest, commonly called the lag time. Calculating the full correlation at full resolution from 100 ns to a few tens of seconds would require excessive calculation and storage time given current memory and processor technology.…”

Section: Introductionmentioning

confidence: 99%

A scalable correlator for multichannel diffuse correlation spectroscopy

et al. 2016

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Diffuse correlation spectroscopy (DCS) is a technique which enables powerful and robust non-invasive optical studies of tissue micro-circulation and vascular blood flow. The technique amounts to autocorrelation analysis of coherent photons after their migration through moving scatterers and subsequent collection by single-mode optical fibers. A primary cost driver of DCS instruments are the commercial hardware-based correlators, limiting the proliferation of multi-channel instruments for validation of perfusion analysis as a clinical diagnostic metric. We present the development of a low-cost scalable correlator enabled by microchip-based time-tagging, and a software-based multi-tau data analysis method. We will discuss the capabilities of the instrument as well as the implementation and validation of 2- and 8-channel systems built for live animal and pre-clinical settings.

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“…We average over the specific tube topology by averaging the bead MSD over the 10 replicas. To efficiently analyze the MSD data spanning a long time range, a multi-τ correlator [36] is implemented. The final results for all three ring lengths are presented in Fig.…”

mentioning

confidence: 99%