Planar radial spots in a three-component FitzHugh-Nagumo system

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.

One-dimensional hydrogen-bonded structures in the 1:1 proton-transfer salts of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine

The crystal structures of the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine, viz. diisopropylaminium 2-carboxy-4,5-dichlorobenzoate (1) and hexamethylenetetraminium 2-carboxy-4,5-dichlorobenzoate hemihydrate (2), have been determined. Crystals of both 1 and 2 are triclinic, space group P-1, with Z = 2 in cells with a = 7.0299(5), b = 9.4712(7), c = 12.790(1)Å, α = 99.476(6), β = 100.843(6), γ = 97.578(6)o (1) and a = 7.5624(8), b = 9.8918(8), c = 11.5881(16)Å, α = 65.660(6), β = 86.583(4), γ = 86.987(8)o (2). In each, one-dimensional hydrogen-bonded chain structures are found: in 1 formed through aminium N+-H...Ocarboxyl cation-anion interactions. In 2, the chains are formed through anion carboxyl O...H-Obridging water interactions with the cations peripherally bound. In both structures, the hydrogen phthalate anions are essentially planar with short intra-species carboxylic acid O-H...Ocarboxyl hydrogen bonds [O…O, 2.381(3) Å (1) and 2.381(8) Å (2)].

Low-dimensional hydrogen-bonded structures in the 1:1 and 1:2 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine

The structures of proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine, namely triethylaminium 2-carboxy-4,5-dichlorobenzoate C~6~H~16~N^+^ C~8~H~3~Cl~2~O~4~^-^ (I), diethylaminium 2-carboxy-4,5-dichlorobenzoate C~4~H~12~N^+^ C~8~H~3~Cl~2~O~4~^-^ (II), bis(n-butylaminium) 4,5-dichlorophthalate monohydrate 2(C~4~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (III) and bis(piperidinium) 4,5-dichlorophthalate monohydrate 2(C~5~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (IV)have been determined at 200 K. All compounds have hydrogen-bonding associations giving in (I) discrete cation-anion units, linear chains in (II) while (III) and (IV) both have two-dimensional structures. In (I) a discrete cation-anion unit is formed through an asymmetric R2/1(4) N+-H...O,O' hydrogen-bonding association whereas in (II), one-dimensional chains are formed through linear N-H...O associations by both aminium H donors. In compounds (III) and (IV) the primary N-H...O linked cation-anion units are extended into a two-dimensional sheet structure via amide N-H...O(carboxyl) and ...O(carbonyl) interactions. In the 1:1 salts [(I) and (II)], the hydrogen 4,5-dichlorophthalate anions are essentially planar with short intramolecular carboxylic acid O-H...O(carboxyl) hydrogen bonds [O...O, 2.4223(14) and 2.388(2)A respectively]. This work provides a further example of the uncommon zero-dimensional hydrogen-bonded DCPA-Lewis base salt and the one-dimensional chain structure type, while even with the hydrate structures of the 1:2 salts with the primary and secondary amines, the low dimensionality generally associated with 1:1 DCPA salts is also found.

Minimising capacitive couplings and distributing copper losses in planar magnetic elements

Planar magnetic elements are becoming a replacement for their conventional rivals. Among the reasons supporting their application, is their smaller size. Taking less bulk in the electronic package is a critical advantage from the manufacturing point of view. The planar structure consists of the PCB copper tracks to generate the desired windings .The windings on each PCB layer could be connected in various ways to other winding layers to produce a series or parallel connection. These windings could be applied coreless or with a core depending on the application in Switched Mode Power Supplies (SMPS). Planar shapes of the tracks increase the effective conduction area in the windings, brings about more inductance compared to the conventional windings with the similar copper loss case. The problem arising from the planar structure of magnetic inductors is the leakage current between the layers generated by a pulse width modulated voltage across the inductor. This current value relies on the capacitive coupling between the layers, which in its turn depends on the physical parameters of the planar scheme. In order to reduce this electrical power dissipation due to the leakage current and Electromagnetic Interference (EMI), reconsideration in the planar structure might be effective. The aim of this research is to address problem of these capacitive coupling in planar layers and to find out a better structure for the planar inductance which offers less total capacitive coupling and thus less thermal dissipation from the leakage currents. Through Finite Element methods (FEM) several simulations have been carried out for various planar structures. The labs prototypes of these structures are built with the similar specification of the simulation cases. The capacitive couplings of the samples are determined with Spectrum Analyser whereby the test analysis verified the simulation results.

Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system

We investigate regions of bistability between different travelling and stationary structures in a planar singularly-perturbed three-component reaction-diffusion system that arises in the context of gas discharge systems. In previous work, we delineated the existence and stabil-ity regions of stationary localized spots in this system. Here, we complement this analysis by establishing the stability regions of planar travelling fronts and stationary stripes. Taken together, these results imply that stable fronts and spots can coexist in three-component systems. Numerical simulations indicate that the stable fronts never move towards stable spots but instead move away from them.

Ordered mixed-layer structures in the Mighei carbonaceous chondrite matrix

High resolution transmission electron microscopy of the Mighei carbonaceous chondrite matrix has revealed the presence of a new mixed layer structure material. This mixed-layer material consists of an ordered arrangement of serpentine-type (S) and brucite-type (B) layers in the sequence ... SBBSBB. ... Electron diffraction and imaging techniques show that the basal periodicity is ~ 17 Å. Discrete crystals of SBB-type material are typically curved, of small size (<1 μm) and show structural variations similar to the serpentine group minerals. Mixed-layer material also occurs in association with planar serpentine. Characteristics of SBB-type material are not consistent with known terrestrial mixed-layer clay minerals. Evidence for formation by a condensation event or by subsequent alteration of preexisting material is not yet apparent. © 1982.

A novel winding structure in planar inductors to decrease overall capacitive couplings

This paper analyses effects of winding structure on capacitive coupling reduction appearing in the planar magnetic elements at high frequencies. Capacitive coupling appears between the conductive layers of the planar transformers resulting in high current spikes and consequently high power dissipation. With finite element analysis, the equivalent capacitive coupling of magnetic elements is calculated for different structures of planar windings. Finally, a new winding structure with minimum capacitive coupling is introduced for the planar magnetic elements, which is verified by simulation and experiments.

Molecular cocrystals of 5-(4-bromophenyl)-1,3,4-thiadiazol-2-amine: hydrogen bonding in the structures of the 1:1 adduct with 2-(naphthalen-2-yloxy)acetic acid and the salt with 3,5-dinitrobenzoic acid

The structures of the anhydrous products from the interaction of 2-amino-5-(4-bromophenyl)-1,3,4-thiadiazole with (2-naphthoxy)acetic acid, the 1:1 adduct C8H6BrN3S . C12H10O3 (I) and 3,5-dinitrobenzoic acid, the salt C8H7BrN3S+ C7H3N2O6- (II) have been determined. In the adduct (I), a heterodimer is formed through a cyclic hydrogen-bonding motif [graph set R2/2(8)], involving carboxylic acid O-H...N(hetero)and amine N-H...O(carboxyl) interactions. The heterodimers are essentially planar with a thiadiazole to naphthyl ring dihedral angle of 15.9(2)deg. and the intramolecular thiadiazole to phenyl ring angle of 4.7(2)deg. An amine N-H...N(hetero) hydrogen bond between the heterodimers generates a one-dimensional chain structure extending down [001]. Also present are weak benzene-benzene and naphthalene-naphthalene pi-pi stacking interactions down the b axis [minimum ring centroid separation, 3.936(3) Ang.]. With the salt (II), the cation-anion association is also through a cyclic R2/2(8) motif but involving duplex N-H...O(carboxyl) hydrogen bonds, giving a heterodimer which is close to planar [dihedral angles between the thiadiazole ring and the two benzene rings, 5.00(16)deg. (intra) and 7.23(15)deg. (inter)]. A secondary centrosymmetric cyclic N-H...O(carboxyl) hydrogen-bonding association involving the second amino H-atom generates a heterotetramer. Also present in the crystal are weak pi-pi i-\p interactions between thiadiazolium rings [minimum ring centroid separation, 3.936(3)Ang.], as well as a short Br...O(nitro) interaction [3.314(4)Ang.]. The two structures reported here now provide a total of three crystallographically characterized examples of co-crystalline products from the interaction of 2-amino-5-(4-bromophenyl)-1,3,4-thiadiazole with carboxylic acids, of which only one involves proton-transfer.

Solitary filamentary structures and nanosecond dynamics in atmospheric-pressure plasmas driven by tailored dc pulses

Nanosecond dynamics of two separated discharge cycles in an asymmetric dielectric barrier discharge is studied using time-resolved current and voltage measurements synchronized with high-speed (∼5 ns) optical imaging. Nanosecond dc pulses with tailored raise and fall times are used to generate solitary filamentary structures (SFSs) during the first cycle and a uniform glow during the second. The SFSs feature ∼1.5 mm thickness, ∼1.9 A peak current, and a lifetime of several hundred nanoseconds, at least an order of magnitude larger than in common microdischarges. This can be used in alternating localized and uniform high-current plasma treatments in various applications.

Self-interaction of high-frequency surface waves in magnetoactive plasma planar waveguide

The nonlinear effect of hf surface waves self-interaction in a magnetoactive planar plasma waveguide is studies. The waveguide structure under consideration can be formed by gaseous or semiconducting homogeneous plasma, which is limited by a perfectly conducting metal surface. The surface (localized near the surface) wave perturbations propagating on the plasma-metal boundary perpendicular to the constant external magnetic field, are investigated. The nonlinear frequency shift connected with interaction of the second harmonic and static surface perturbations with the main frequency wave, is determined using the approximation of weak nonlinearity. It is shown that the process of double-frequency signal generation is the dissipative one as a result of bulk wave excitation on the surface wave second harmonic.

Crystal structures and hydrogen-bonding in the co-crystalline adducts of 3,5-dinitrobenzoic acid with 4-aminosalicylic acid and 2-hydroxy-3-(1H-indol-3-yl)propenoic acid

The structures of the cocrystalline adducts of 3,5-dinitrobenzoic acid (3,5-DNBA) with 4-aminosalicylic acid (PASA), the 1:1 partial hydrate, C7H4N2O6 .C7H7NO3 . 2H2O, (I) and 2-hydroxy-3-(1H-indol-3-yl)propenoic acid (HIPA) and the 1:1:1 d6-dimethylsulfoxide solvate, C7H4N2O6 . C11H9NO3 . C2D6OS, (II) are reported. The crystal substructure of (I) comprises two centrosymmetric hydrogen-bonded R2/2(8) homodimers, one with 3,5-DNBA, the other with PASA, and an R2/2(8) 3,5-DNBA-PASA heterodimer. In the crystal, inter-unit amine N-H...O and water O-H...O hydrogen bonds generate a three-dimensional supramolecular structure. In (II), the asymmetric unit consists of the three constituent molecules which form an essentially planar cyclic hydrogen-bonded heterotrimer unit [graph set R2/3(17)] through carboxyl, hydroxy and amino groups. These units associate across a crystallographic inversion centre through the HIPA carboxylic acid group in an R2/2~(8) hydrogen-bonding association, giving a zero-dimensional structure lying parallel to (100). In both structures, pi--pi interactions are present [minimum ring centroid separations: 3.6471(18)A in (I) and 3.5819(10)A in (II)].

Crystal structures of the co-crystalline adduct 5-(4-bromophenyl)-1,3,4-thiadiazol-2-amine--4-nitrobenzoic acid (1/1) and the salt 2-amino-5-(4-bromophenyl)-1,3,4-thiadiazol-3-ium 2-carboxy-4,6-dinitrophenolate

The structures of the 1:1 co-crystalline adduct C8H6BrN3S . C7H5NO4 (I) and the salt C8H7BrN3S+ C7H3N2O7- (II) from the interaction of 5-(4-bromophenyl)-1,3,4-thiadiazol-2-amine with 4-nitrobenzoic acid and 3,5-dinitrosalicylic acid, respectively, have been determined. The primary inter-species association in both (I) and (II) is through duplex R2/2(8) (N-H...O/O-H...O) or (N-H...O/N-H...O) hydrogen bonds, respectively, giving heterodimers. In (II), these are close to planar [dihedral angles between the thiadiazole ring and the two phenyl rings are 2.1(3)deg. (intra) and 9.8(2)deg. (inter)], while in (I) these angles are 22.11(15) and 26.08(18)deg., respectively. In the crystal of (I), the heterodimers are extended into a one-dimensional chain along b through an amine N-...N(thiadiazole) hydrogen bond but in (II), a centrosymmetric cyclic heterotetramer structure is generated through N-H...O hydrogen bonds to phenol and nitro O-atom acceptors and features, together with the primary R2/2(8) interaction, conjoined R4/6(12), R2/1(6) and S(6) ring motifs. Also present in (I) are pi--pi interactions between thiadiazole rings [minimum ring centroid separation, 3.4624(16)deg.] as well as short Br...O(nitro) interactions in both (I) and (II) [3.296(3)A and 3.104(3)A, respectively].

Model updating of real structures with ambient vibration data

It is important to develop reliable finite element models for real structures not only in the design phase but also for the structural health monitoring and structural maintenance purposes. This paper describes the experience of the authors in using ambient vibration model identification techniques together with model updating tools to develop reliable finite element models of real civil engineering structures. Case studies of two real structures are presented in this paper. One is a 10 storey concrete building which is considered as a non-slender structure with complex boundary conditions. The other is a single span concrete foot bridge which is also a relatively inflexible planar structure with complex boundary conditions. Both structures are located at the Queensland University of Technology (QUT) and equipped with continuous structural health monitoring systems.