The use of Herschel–Quincke tubes to improve the efficiency of lined ducts

The scattering matrix results of Herschel–Quincke (HQ) resonators installed in combination with an acoustic liner (HQ-Liners) are presented in this paper. This approach aims at controlling both tonal and broadband noise to improve the liner efficiency. It uses circumferential arrays of Herschel–Quincke tubes on a main duct in a serial association with a locally reacting liner of known impedance. Results for the scattering matrix of this system are deduced from an analytical model and compared with experimental and numerical data showing a good agreement. Analysis of the scattering matrix coefficients points out the modal conversion properties that depend on the number of HQ tubes along the circumference. Results of the transmission loss show that the choice of an optimal HQ configuration with respect to the liner properties can substantially improve the liner efficiency.     

A Note on Toeplitz’ Conjecture

In 1911, Toeplitz made a conjecture asserting that every Jordan curve in $\mathbb{R}^{2}$ contains four points forming the corners of a square. Here Conjecture C is presented, which states that the side length of the largest square on a closed curve that consists of edges of an n×n grid is at least $1/\sqrt{2}$ times the side length of the largest axis-aligned square contained inside the curve. Conjecture C implies Toeplitz’ conjecture and is verified computationally for n≤13.     

Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.     

Modelling the Flow of Carbon Dioxide Through Beds of Cereal Grains

The insect population in grain stores can be kept under control by maintaining a high concentration of CO₂ gas (greater than 35%) throughout the grain bed. In this paper the initial phase of this process is considered, where the gas is introduced into the bed. The flow of CO₂ through the grain bulk is modelled as fluid flow in a porous medium and the effect of advection, dispersion, sorption and curvilinear isobars and streamlines are considered. An analytic solution to this problem is developed using perturbation expansions and the analysis is restricted to the dominant term in each expansion. In curvilinear flow, a useful variable is the traverse time; the time taken for the gas to travel from the inlet duct. It is shown that lines of constant traverse time are also lines of constant CO₂ concentration throughout the grain bed except in the narrow region called the front, where the concentration gradient is large. For most grain stores the isobars have a negative curvature and in these situations the front moves more slowly than in uniform flow and the width of the front increases more rapidly as it travels through the grain bed. It is shown that sorption has an effect on the CO₂ concentration in the air for some grains such as canola but not for others such as wheat.     

Electron impact induced fragmentations of some 2,2-disubstituted 1,3-oxathiolanes

The electron impact induced fragmentations of nine 2,2-disubstituted 1,3-oxathiolanes have been studied by means of exact mass measurement and metastable ion analysis. The ring cleavage almost always takes place so that the C(2)? S and C(5)? O bonds are broken, leading to the most stable products. The nature of the substituents determines the primary fragmentations of molecular ions. Ring cleavage is important only if both substituents are alkyl groups or if the carbon attaching to the ring has an alkyl character. The loss of the substituent becomes the most favourable process if it is attached to the ring through the electron-deficient carbon atom.     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

PCMSolver: An open-source library for solvation modeling

PCMSolver is an open-source library for continuum electrostatic solvation. It can be combined with any quantum chemistry code and requires a minimal interface with the host program, greatly reducing programming effort. As input, PCMSolver needs only the molecular geometry to generate the cavity and the expectation value of the molecular electrostatic potential on the cavity surface. It then returns the solvent polarization back to the host program. The design is powerful and versatile: minimal loss of performance is expected, and a standard single point self-consistent field implementation requires no more than 2 days of work. We provide a brief theoretical overview, followed by two tutorials: one aimed at quantum chemistry program developers wanting to interface their code with PCMSolver , the other aimed at contributors to the library. We finally illustrate past and ongoing work, showing the library's features, combined with several quantum chemistry programs.     

Effect of Trichoderma reesei Proteinases on the Affinity of an Inorganic-Binding Peptide

An inorganic-binding peptide sequence with high affinity to silica-containing materials was fused to a glycoside hydrolase GH26 mannanase, ManA, from the extremely thermophilic bacterium Dictyoglomus thermophilum. The resulting recombinant enzyme produced in Escherichia coli, ManA-Linker, displayed high binding affinity towards synthetic zeolite while retaining its catalytic activity at 80 °C. ManA-Linker was able to bind to the zeolite at different pH levels, indicating a true pH-independent binding. However, complete degradation of the peptide linker was observed when the recombinant ManA-Linker was exposed to the supernatant from the filamentous fungus Trichoderma reesei. This degradation was caused by extracellular proteinases produced by T. reesei during its growth phase. Several derivatives of ManA-Linker were designed and expressed in E. coli. All the derivatives carrying a single sequence of the linker were still susceptible to T. reesei proteinase degradation. Complete substitution of the linker sequence by (GGGGS)₁₆ resulted in a proteinase-resistant ManA derivative, ManA-Linker-(GGGGS)₁₆, which was able to bind to zeolite in a pH-dependent manner.     

A compact olfactometer for IMS measurements and testing human perception

Production of easily controllable and measurable odor stimuli is needed when studying human olfaction, olfaction-related physiology and psychological reactions to odors. Controlled odor producing instruments are called olfactometers. For testing and calibrating new olfactometers or sensor arrays, a reliable input signal has to be produced to verify their accurate functionality. A common input signal in various olfactometers has been the use of volatile organic compounds (VOCs) in gaseous form. We present a compact olfactometer able to produce controlled continuous odor stimuli from three individual channels. For measuring the output gas flow, we used a ChemPro 100i (Environics, Finland) device that is based on aspiration ion mobility spectrometry (aIMS). IMS is a robust and sensitive method for measuring VOCs and is used especially in detecting toxic industrial chemicals and chemical warfare agents, but the technology is also suitable for other olfactory-related applications. The olfactometer was used to produce synthetic jasmine scent using three main odor components from jasmine oil and all the components were diluted using propylene glycol. The dilutions were supplied to the system using programmable syringe pumps, which guided the dilutions to individual evaporation units. We conducted experiments to verify the functionality of our olfactometer. Analysis of the ChemPro100i data showed that olfactometer can use different odor components to produce continuous, stable output flows with controlled concentrations.     

Broadband noise reduction by circular multi-cavity mufflers operating in multimodal propagation conditions

In this study, sound propagation through a circular duct with non-locally lining is investigated both numerically and experimentally. The liner concept is based on perforated screens backed by air cavities. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. This gives rise to complex scattering mechanisms among duct modes which renders the muffler more effective over a broader frequency range. This work emanates from the Cleansky European HEXENOR project which aim is to identify the best multi-cavity muffler configuration for reduction of exhaust noise from helicopter turboshaft engines. Here, design parameters are the cavity dimensions in both longitudinal and azimuthal directions. The best cavity configuration must in addition fit weight specifications which implies that the number of walls separating each cavity should be chosen as small as possible. To achieve these objectives, the scattering matrix of the lined duct section is obtained experimentally for two specific muffler configurations operating in multimodal propagation conditions. The good agreement with numerical predictions serves to validate the perforate plate impedance model used in our calculation. Finally, given an incident acoustic pressure which is representative of typical combustion noise spectrum, the best cavity configuration achieving the maximum overall acoustic Transmission Loss is selected numerically. The study also illustrates how the acoustic performances are dependent on the nature of the incident field.