Three-dimensional Icosahedral Phase Field Quasicrystal

We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation

Which Wave Numbers Determine the Thermodynamic Stability of Soft Matter Quasicrystals?

For soft matter to form quasicrystals an important ingredient is to have two characteristic length scales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wave numbers should be favored, and the ratio of these wave numbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wave numbers can be involved, other wave numbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials that can suppress or encourage density modes with wave numbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems

Density Distribution in Soft Matter Crystals and Quasicrystals

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centered on lattice sites or via a Fourier sum. Here, we argue that representing instead the logarithm of the density distribution via a Fourier sum is better. We show that truncating such a representation after only a few terms can be highly accurate for soft matter crystals. For quasicrystals, this sum does not truncate so easily, nonetheless, representing the density profile in this way is still of great use, enabling us to calculate the phase diagram for a three-dimensional quasicrystal-forming system using an accurate nonlocal density functional theory

Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation

We investigate the liquid state structure of the two-dimensional model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focusing on the radial distribution function g(r) and its asymptotic decay r→∞. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is ≈1.932. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the nonequilibrium growth or decay of small-amplitude density fluctuations in a bulk fluid

Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each. One approximation that is made in standard derivations is to neglect a term of form ∇⋅[n∇Ln], where n is the scaled density profile and L is a linear operator. We show that this term makes a significant contribution to the stability of the crystal, and that dropping this term from the theory forces another approximation, that of replacing the logarithmic term from the ideal gas contribution to the free energy with its truncated Taylor expansion, to yield a polynomial in n. However, the consequences of doing this are (i) the presence of an additional spinodal in the phase diagram, so the liquid is predicted first to freeze and then to melt again as the density is increased; and (ii) other periodic structures, such as stripes, are erroneously predicted to be thermodynamic equilibrium structures. In general, L consists of a nonlocal convolution involving the pair direct correlation function. A second approximation sometimes made in deriving PFC theory is to replace L with a gradient expansion involving derivatives. We show that this leads to the possibility of the density going to zero, with its logarithm going to −∞ while being balanced by the fourth derivative of the density going to +∞. This subtle singularity leads to solutions failing to exist above a certain value of the average density. We illustrate all of these conclusions with results for a particularly simple model two-dimensional fluid, the generalized exponential model of index 4 (GEM-4), chosen because a DDFT is known to be accurate for this model. The consequences of the subsequent PFC approximations can then be examined. These include the phase diagram being both qualitatively incorrect, in that it has a stripe phase, and quantitatively incorrect (by orders of magnitude) regarding the properties of the crystal phase. Thus, although PFC models are very successful as phenomenological models of crystallization, we find it impossible to derive the PFC as a theory for the (scaled) density distribution when starting from an accurate DDFT, without introducing spurious artifacts. However, we find that making a simple one-mode approximation for the logarithm of the density distribution lnρ(x) rather than for ρ(x) is surprisingly accurate. This approach gives a tantalizing hint that accurate PFC-type theories may instead be derived as theories for the field lnρ(x), rather than for the density profile itself

Low dose gamma irradiation does not affect the quality or total ascorbic acid concentration of “sweetheart” passionfruit (passiflora edulis)

Passionfruit (Passiflora edulis, Sims, cultivar “Sweetheart”) were subject to gamma irradiation at levels suitable for phytosanitary purposes (0, 150, 400 and 1000 Gy) then stored at 8 °C and assessed for fruit quality and total ascorbic acid concentration after one and fourteen days. Irradiation at any dose (≤1000 Gy) did not affect passionfruit quality (overall fruit quality, colour, firmness, fruit shrivel, stem condition, weight loss, total soluble solids level (TSS), titratable acidity (TA) level, TSS/TA ratio, juice pH and rot development), nor the total ascorbic acid concentration. The length of time in storage affected some fruit quality parameters and total ascorbic acid concentration, with longer storage periods resulting in lower quality fruit and lower total ascorbic acid concentration, irrespective of irradiation. There was no interaction between irradiation treatment and storage time, indicating that irradiation did not influence the effect of storage on passionfruit quality. The results showed that the application of 150, 400 and 1000 Gy gamma irradiation to “Sweetheart” purple passionfruit did not produce any deleterious effects on fruit quality or total ascorbic acid concentration during cold storage, thus supporting the use of low dose irradiation as a phytosanitary treatment against quarantine pests in purple passionfruit. © 2015 MDPI.Open access retrieved from: https://www.mdpi.com/2304-8158/4/3/37

Editorial: Extreme Events in the Developing World

This Research Topic “Extreme Events in the Developing World” showcases a selection of articles that develop our knowledge of extreme events in the developing world. Papers range from those presenting recent evidence for and future likelihood of changes in the occurrence and exposure to extreme events, together with examples of the impacts of extreme events in a variety of sectors. Papers also consider the range of climate services responses to this challenge, highlighting the need for new types of weather and climate information, new methods of producing and communicating that information in order to reduce risk, as well as providing some key examples of success stories, with a particular focus on Africa. Our intention here is to balance some of the bad news with what might work, and how we might learn from such examples.UK Natural Environment Research Council (NERC); UK Government’s Department for International Development (DFID); UKRI Global Challenges Research Fund Africa-SWIFT project; NASA GPM project.https://www.frontiersin.org/journals/climatedm2022Geography, Geoinformatics and Meteorolog

Flavour Physics in the Soft Wall Model

We extend the description of flavour that exists in the Randall-Sundrum (RS) model to the soft wall (SW) model in which the IR brane is removed and the Higgs is free to propagate in the bulk. It is demonstrated that, like the RS model, one can generate the hierarchy of fermion masses by localising the fermions at different locations throughout the space. However, there are two significant differences. Firstly the possible fermion masses scale down, from the electroweak scale, less steeply than in the RS model and secondly there now exists a minimum fermion mass for fermions sitting towards the UV brane. With a quadratic Higgs VEV, this minimum mass is about fifteen orders of magnitude lower than the electroweak scale. We derive the gauge propagator and despite the KK masses scaling as $m_n^2\sim n$, it is demonstrated that the coefficients of four fermion operators are not divergent at tree level. FCNC's amongst kaons and leptons are considered and compared to calculations in the RS model, with a brane localised Higgs and equivalent levels of tuning. It is found that since the gauge fermion couplings are slightly more universal and the SM fermions typically sit slightly further towards the UV brane, the contributions to observables such as $\epsilon_K$ and $\Delta m_K$, from the exchange of KK gauge fields, are significantly reduced.Comment: 33 pages, 15 figures, 5 tables; v2: references added; v3: modifications to figures 4,5 and 6. version to appear in JHE

Asymmetrical seeding of MSCs into fibrin–poly(ester‐urethane) scaffolds and its effect on mechanically induced chondrogenesis

Mesenchymal stem cells (MSCs) are currently being investigated as candidate cells for regenerative medicine approaches for the repair of damaged articular cartilage. For these cells to be used clinically, it is important to understand how they will react to the complex loading environment of a joint in vivo. In addition to investigating alternative cell sources, it is also important for the structure of tissue‐engineered constructs and the organization of cells within them to be developed and, if possible, improved. A custom built bioreactor was used to expose human MSCs to a combination of shear and compression loading. The MSCs were either evenly distributed throughout fibrin‐poly(ester‐urethane) scaffolds or asymmetrically seeded with a small proportion seeded on the surface of the scaffold. The effect of cell distribution on the production and deposition of cartilage‐like matrix in response to mechanical load mimicking in vivo joint loading was then investigated. The results show that asymmetrically seeding the scaffold led to markedly improved tissue development based on histologically detectable matrix deposition. Consideration of cell location, therefore, is an important aspect in the development of regenerative medicine approaches for cartilage repair. This is particularly relevant when considering the natural biomechanical environment of the joint in vivo and patient rehabilitation protocols