Optimized extraction of soluble defatted rice bran fiber and its application for microencapsulation of fish oil

Defatted rice bran (DRB) is a byproduct of rice milling and rice bran oil extraction. Soluble rice bran fiber (SRBF) extracted from defatted rice bran is known for its antioxidant activity and hypocholesterolemic effects in human, while purified menhaden oil (PMO) is a good source of eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). The goal of the study was to estimate optimum extraction conditions to extract SRBF from DRB, develop a cost effective method to purify SRBF and produce microencapsulated PMO with SRBF. The response surface methodology showed that an estimated optimum yield of SRBF (7.89%) could be extracted from DRB with 3% Ca(OH)2 solution to DRB ratio 29.75:1 and stirred for 1 hr at 84oC and also Ca(OH)2 solution concentration was the most effective factor among the conditions used to extract SRBF. Our study showed that conventional processing steps, such as dialysis and alcohol precipitation, for removing mineral and monosaccharides and other small molecules from SRBF, could be replaced with the ultrafiltration technology. The ultrafiltration for purifying SRBF solution at 100 kPa with 10 kDa MWCO membrane required less time than filtering the solution at the same pressure with 1 and 5 kDa MWCO membranes. The estimated microencapsulated PMO with SRBF powder (MFMO) production rate using spray dryer was 3.45 * 10-5 kg dry solids/s and was higher than the actual production rate 2.31 * 10-5 kg dry solids/s. The energy required to increase the inlet ambient air temperature from 27.1 to 180 oC and evaporation rate for spray drying the emulsion was 2.78 kJ/s and 7.8 * 10-3 kg water/s, respectively. EPA and DHA contents of MFMO were 11.52% and 4.51%, respectively. The particle size of 90% MFMO ranged from 8 to 62 um, and the volume-length diameter of MFMO was 28.5 um. The study demonstrated that optimum extraction conditions for extracting SRBF from DRB could be achieved through the response surface methodology, conventional purification steps of SRBF including dialysis and alcohol precipitation could be replaced with ultrafiltration technology, and the MFMO could be provided with potential health benefits for humans

Anyon exclusions statistics on surfaces with gapped boundaries

An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but boundaries often appear in real-life materials. When fusion of anyons is involved, certain `pseudo-species' anyons appear in the exotic statistical weights of non-Abelian anyon systems; however, the meaning and significance of pseudo-species remains an open problem. In this paper, we propose an extended anyon exclusion statistics on surfaces with gapped boundaries, introducing mutual exclusion statistics between anyons as well as the boundary components. Motivated by Refs. [2, 3], we present a formula for the statistical weight of many-anyon states obeying the proposed statistics. We develop a systematic basis construction for non-Abelian anyons on any Riemann surfaces with gapped boundaries. From the basis construction, we have a standard way to read off a canonical set of statistics parameters and hence write down the extended statistical weight of the anyon system being studied. The basis construction reveals the meaning of pseudo-species. A pseudo-species has different `excitation' modes, each corresponding to an anyon species. The `excitation' modes of pseudo-species corresponds to good quantum numbers of subsystems of a non-Abelian anyon system. This is important because often (e.g., in topological quantum computing) we may be concerned about only the entanglement between such subsystems.Comment: 36 pages, 14 figure

Boundary Hamiltonian theory for gapped topological phases on an open surface

In this paper we propose a Hamiltonian approach to gapped topological phases on an open surface with boundary. Our setting is an extension of the Levin-Wen model to a 2d graph on the open surface, whose boundary is part of the graph. We systematically construct a series of boundary Hamiltonians such that each of them, when combined with the usual Levin-Wen bulk Hamiltonian, gives rise to a gapped energy spectrum which is topologically protected; and the corresponding wave functions are robust under changes of the underlying graph that maintain the spatial topology of the system. We derive explicit ground-state wavefunctions of the system and show that the boundary types are classified by Morita-equivalent Frobenius algebras. We also construct boundary quasiparticle creation, measuring and hopping operators. These operators allow us to characterize the boundary quasiparticles by bimodules of Frobenius algebras. Our approach also offers a concrete set of tools for computations. We illustrate our approach by a few examples.Comment: 21 pages;references correcte

Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are compatible with the bulk Hamoltonian. Given the bulk Hamiltonian defined by a gauge group $G$ and a four-cocycle $\omega$ in the fourth cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a three-cochain $\alpha$ in the third cochain group of $K$ over $U(1)$. The boundary Hamiltonian to be constructed must be gapped and invariant under the topological renormalization group flow (via Pachner moves), leading to a generalized Frobenius condition. Given $K$, a solution to the generalized Frobenius condition specifies a gapped boundary condition. We derive a closed-form formula of the ground state degeneracy of the model on a three-cylinder, which can be naturally generalized to three-spaces with more boundaries. We also derive the explicit ground-state wavefunction of the model on a three-ball. The ground state degeneracy and ground-state wavefunction are both presented solely in terms of the input data of the model, namely, $\{G,\omega,K,\alpha\}$

Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae

We investigate interdomain excitations in composite systems of topological orders separated by gapped domain walls. We derive two domain-wall Verlinde formulae that relate the braiding between interdomain excitations and domain-wall quasiparticles to the fusion rules of interdomain excitations and the fusion rules of domain-wall quasiparticles. We show how to compute such braiding and fusion with explicit non-Abelian examples and find that the fusion rules of interdomain excitations are generally fractional or irrational. By exploring the correspondence between composite systems and anyon condensation, we uncover why such fusion rules should be called symmetry fractionalized (irrationalized) fusion rules. Our domain-wall Verlinde formulae generalize the Verlinde formula of a single topological order and the defect Verlinde formula found in [C. Shen and L.-Y. Hung, Phys. Rev. Lett. 123, 051602 (2019)]. Our results may find applications in topological quantum computing, topological field theories, and conformal field theories.Comment: 13 pages, 7 figure

Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries

In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group $G$) of three-dimensional topological orders. We find that the gapped boundary condition of the gauge theory model is characterized by a Frobenius algebra in the representation category $\mathcal Rep(G)$ of $G$, which also describes the charge splitting and condensation on the boundary. We also show that our Fourier transform maps the three-dimensional gauge theory model with input data $G$ to the Walker-Wang model with input data $\mathcal Rep(G)$ on a trivalent lattice with dangling edges, after truncating the Hilbert space by projecting all dangling edges to the trivial representation of $G$. This Fourier transform also provides a systematic construction of the gapped boundary theory of the Walker-Wang model. This establishes a correspondence between two types of topological field theories: the extended Dijkgraaf-Witten and extended Crane-Yetter theories.Comment: 39 pages, 9 figure