Hydrodynamic fluctuations in the presence of one parameter Mittag-Leffler friction

The effects of hydrodynamic fluctuations on the subdiffusive motion of a particle subject to one parameter Mittag-Leffler friction are examined by means of the fractional Langevin equation. The particle experiences an overall additive colored noise formed by, on the one hand, the hydrodynamic back flow effects and, on the other hand, an additional contribution predicted by fluctuation dissipation relation. Particle motion may or may not be subject to a restoring force. All possible combinations of forces exerted on the test particle are being studied, and for each of them the generalized response function in terms of multinomial Mittag-Leffler functions is provided. Mean square displacement, normalized velocity and position auto-correlation functions are furnished as special cases of the generalized response function, and their short and long time limits are analytically given. In addition, for the same measures analytical expressions valid for time windows much broader than the usual asymptotic limit are provided, and can be used to fit real life data. We demonstrate that normalized velocity and position auto-correlation functions are the main sources providing information on the effect of hydrodynamic fluctuations on particle motion. Actually, they oppose to friction and to restoring force, and smooth out the anti-persistent character of the motion

Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions

White noise is fundamentally linked to many processes; it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise

Statistics of low-energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study

Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by non-zero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states (the states with no nodes within their localization segments) that are localized at different segments has zero mean and shows almost no repulsion. The typical width of the latter distribution is of the same order as the typical spacing in the local discrete energy structure, so that this local structure is hidden; it does not reveal itself neither in the density of states nor in the linear absorption spectra. However, this structure affects the two-exciton transitions involving the states of the same segment and can be observed by the pump-probe spectroscopy. We analyze also the disorder degree scaling of the first and second momenta of the distributions.Comment: 10 pages, 6 figure

Microstructure and reconstitution of freeze-dried gum Arabic at a range of concentrations and primary drying temperatures

Freeze-drying is an energy intensive unit operation used for the production of dehydrated foods, such as instant coffee and dried fruits, and results in high sensorial, nutritional and reconstitution properties of the final products. Understanding the relationships between operating conditions and product quality is essential to design processes that are energy efficient, whilst producing high quality dried foods. In this work, the properties (microstructure and reconstitution) of freeze-dried gum arabic samples (with initial concentrations ranging between 20 and 60% solids by weight) were evaluated. The materials were dried at three different primary drying shelf temperatures, Ts (- 20, - 30 and - 40 ◦C). Sample temperatures recorded throughout freeze-drying were close to the pre-set Ts, with the exception of the 60% initial concentration system, where the sample was hotter than the shelf by 10–15 ◦C, in particular on increasing Ts. This was attributed to a combination of local temperature and pressure conditions that may have resulted in partial melting of the material. For the 20–50% systems, the properties of the freeze-dried materials were mainly affected by the initial concentration of the system, with increasing initial concentration generally resulting in lower porosities (ranging between 20 and 40%) and higher reconstitution times (ranging between 0.5 and 10min for 95% reconstitution). Pores were generally needle-shaped and <200 μm. Large (200–1800 μm), circular pores were observed in high initial concentration systems, and they were dominant in the microstructure of the freeze-dried 60% sample. The presence of these large bubbles was linked to the partial melting of the material, which enabled its expansion and puffing. For the 60% system, primary drying temperature had a profound effect on the properties of the freeze-dried solid, with samples dried at higher temperature showing higher porosity (e.g. 60–70% for Ts = -¬¬ 20◦C) and faster reconstitution rates (e.g. 3min for 95% reconstitution at Ts = - 20◦C). Overall, this study demonstrates the significance of formulation and shelf temperature on the porous structure of freeze-dried samples, which directly influences product performance

Crystallisation in concentrated systems:a modelling approach

AbstractWater crystallisation in concentrated systems has been studied using a combination of mathematical modelling and experimental work. Two different freezing models have been employed to describe primary and secondary mechanisms (i.e. non-seeded and seed-induced processes, respectively) in sucrose solutions up to 60% (w/w). Differential Scanning Calorimetry (DSC) has been employed to characterise the phase change of the binary water–sucrose system in primary processes, and the kinetic and thermodynamic parameters obtained were coupled to the heat transfer equation to obtain the product temperature distribution. A recently developed method has been also employed to measure crystal growth rates in seed-induced crystallisation systems. Simulated results for the secondary crystallisation mechanism were able to reproduce experimentally observed trends for growth rates. An evaluation of the energy consumption during freezing/crystallisation processes has been carried out to assess each mechanism performance (crystallisation will occur at temperatures approximately 20°C higher in seeded processes) considering different process conditions and product formulations (i.e. solids and air fractions)

Supramolecular interactions in clusters of polar and polarizable molecules

We present a model for molecular materials made up of polar and polarizable molecular units. A simple two state model is adopted for each molecular site and only classical intermolecular interactions are accounted for, neglecting any intermolecular overlap. The complex and interesting physics driven by interactions among polar and polarizable molecules becomes fairly transparent in the adopted model. Collective effects are recognized in the large variation of the molecular polarity with supramolecular interactions, and cooperative behavior shows up with the appearance, in attractive lattices, of discontinuous charge crossovers. The mean-field approximation proves fairly accurate in the description of the gs properties of MM, including static linear and non-linear optical susceptibilities, apart from the region in the close proximity of the discontinuous charge crossover. Sizeable deviations from the excitonic description are recognized both in the excitation spectrum and in linear and non-linear optical responses. New and interesting phenomena are recognized near the discontinuous charge crossover for non-centrosymmetric clusters, where the primary photoexcitation event corresponds to a multielectron transfer.Comment: 14 pages, including 11 figure

Non-invasive predictors of axillary lymph node burden in breast cancer: a single-institution retrospective analysis

Purpose: Axillary staging is an important prognostic factor in breast cancer. Sentinel lymph node biopsy (SNB) is currently used to stage patients who are clinically and radiologically node-negative. Since the establishment that axillary node clearance (ANC) does not improve overall survival in breast-conserving surgery for patients with low-risk biological cancers, axillary management has become increasingly conservative. This study aims to identify and assess the clinical predictive value of variables that could play a role in the quantification of axillary burden, including the accuracy of quantifying abnormal axillary nodes on ultrasound. Methods: A retrospective analysis was conducted of hospital data for female breast cancer patients receiving an ANC at our centre between January 2018 and January 2020. The reference standard for axillary burden was surgical histology following SNB and ANC, allowing categorisation of the patients under ‘low axillary burden’ (2 or fewer pathological macrometastases) or ‘high axillary burden’ (> 2). After exploratory univariate analysis, multivariate logistic regression was conducted to determine relationships between the outcome category and candidate predictor variables: patient age at diagnosis, tumour focality, tumour size on ultrasound and number of abnormal lymph nodes on axillary ultrasound. Results: One hundred and thirty-five patients were included in the analysis. Logistic regression showed that the number of abnormal lymph nodes on axillary ultrasound was the strongest predictor of axillary burden and statistically significant (P = 0.044), with a sensitivity of 66.7% and specificity of 86.8% (P = 0.011). Conclusion: Identifying the number of abnormal lymph nodes on preoperative ultrasound can help to quantify axillary nodal burden and identify patients with high axillary burden, and should be documented as standard in axillary ultrasound reports of patients with breast cancer

Nuclear magnetic resonance and small-angle X-ray scattering studies of mixed sodium dodecyl sulfate and N,N-dimethyldodecylamine N-oxide aqueous systems performed at low temperatures

Surfactant crystallisation is important in many applications in the food, consumer product and medical sectors. However, these processes are not well understood. In particular, surfactant crystallisation can be detrimental to the stability of detergent formulations, such as dish liquid products, resulting in a turbid solution that fails appearance criteria. With the rising global demand for detergent products, understanding the factors that influence formulation stability is of increasing importance. To enable industry to build more robust formulations, it is important to understand the underlying chemistry of the crystallisation process. Here, a model system containing anionic (sodium dodecyl sulfate, SDS) and amphoteric (N,N-dimethyldodecylamine N-oxide, DDAO) surfactants, at concentrations typical of dish liquid products, is studied. Variable temperature 1H nuclear magnetic resonance (NMR) spectroscopy and small-angle X-ray scattering (SAXS) is used to probe the compositional and structural properties of this system, as a function of pH. On cooling, at pH 9, a mixture of hydrated crystals, predominately composed of SDS, and micelles containing both surfactants, have been observed prior to complete freezing. At pH 2, both surfactants appear to undergo a simultaneous phase transition, resulting in the removal of micelles and the formation of hydrated crystals of mixed composition