Browsing by Author "Cooper S"

Now showing 1 - 4 of 4
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    Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions
    (AIP Publishing LLC, 2025-09-07) Robles-Navarro A; Cooper S; Buchheit AA; Busse JK; Burrows A; Smits O; Schwerdtfeger P
    Three-body interactions have long been conjectured to play a crucial role in the stability of matter. However, rigorous studies have been scarce due to the computational challenge of evaluating small energy differences in high-dimensional lattice sums. This work provides a rigorous analysis of Bain-type cuboidal lattice transformations, which connect the face-centered cubic (fcc), mean-centered cubic (mcc), body-centered cubic (bcc), and axially centered cubic (acc) lattices. Our study incorporates a general (n, m) Lennard-Jones (LJ) two-body potential and a long-range repulsive Axilrod-Teller-Muto (ATM) three-body potential. The two-body lattice sums and their meromorphic continuations are evaluated to full precision using super-exponentially convergent series expansions. Furthermore, we introduce a novel approach to computing three-body lattice sums by converting the multi-dimensional sum into an integral involving products of Epstein zeta functions. This enables us to evaluate three-body lattice sums and their meromorphic continuations to machine precision within minutes on a standard laptop. Using our computational framework, we analyze the stability of cuboidal lattice phases relative to the close-packed fcc structure along a Bain transformation path for varying ATM coupling strengths. We analytically demonstrate that the ATM cohesive energy exhibits an extremum at the bcc phase and show numerically that it corresponds to a minimum for repulsive three-body forces along the Bain path. Our results indicate that strong repulsive three-body interactions can destabilize the fcc phase and render bcc energetically favorable for soft LJ potentials. However, even in this scenario, the bcc phase remains susceptible to further cuboidal distortions. These results suggest that the stability of the bcc phase is, besides vibrational, temperature, and pressure effects, strongly influenced by higher than two-body forces. Because of the wrong short-range behavior of the triple-dipole ATM model, the LJ potential is limited to exponents n > 9 for the repulsive wall, otherwise one observes distortion into a set of linear chains collapsing to the origin.
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    Factorizations of theta function identities
    (New Zealand Mathematical Society & University of Auckland, 28/08/2017) Cooper S; Lam HY
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    The Madelung constant in N dimensions
    (Royal Society, 2022-11-30) Burrows A; Cooper S; Schwerdtfeger P
    We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N-dimensional Madelung constants, MN(s), where s is the exponent of the Madelung series (usually chosen as s=1/2). The convergence of the Bessel function expansion is discussed in detail. Values for MN(s) for s=1/2,3/2,3 and 6 for dimension up to N=20 are presented. This work extends Zucker's original analysis on N-dimensional Madelung constants for even dimensions up to N=8.
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    Validity and reliability of Raman spectroscopy for carotenoid assessment in cattle skin
    (Elsevier BV, 2021-09) Mehta M; Naffa R; Zhang W; Schreurs NM; Waterland M; Cooper S; Holmes G
    Carotenoids are powerful antioxidants capable of helping to protect the skin from the damaging effects of exposure to sun by reducing the free radicals in skin produced by exposure to ultraviolet radiation, and they may also have a physical protective effect in human skin. Since carotenoids are lipophilic molecules which can be ingested with the diet, they can accumulate in significant quantities in the skin. Several studies on humans have been conducted to evaluate the protective function of carotenoids against various diseases, but there is very limited published information available to understand the mechanism of carotenoid bioavailability in animals. The current study was conducted to investigate the skin carotenoid level (SCL) in two cattle skin sets - weaners with an unknown feeding regime and New Generation Beef (NGB) cattle with monitored feed at three different ages. Rapid analytical and sensitive Raman spectroscopy has been shown to be of interest as a powerful technique for the detection of carotenoids in cattle skin due to the strong resonance enhancement with 532 nm laser excitation. The spectral difference of both types of skin were measured and quantified using univariate and linear discriminant analysis. SCL was higher in NGB cattle than weaners and there is a perfect classification accuracy between weaners and NGB cattle skin using carotenoid markers as a basis. Further work carried out on carotenoid rich NGB cattle skin of 8, 12 and 24 months of age identified an increasing trend in SCL with age. The present work validated the ability of Raman spectroscopy to determine the skin carotenoid level in cattle by comparing it with established HPLC methods. There is an excellent correlation of R2 = 0.96 between the two methods that could serve as a model for future application for larger population studies.