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Pinned fluxons in a Josephson junction with a finite-length inhomogeneity
- GIANNE DERKS, ARJEN DOELMAN, CHRISTOPHER J. K. KNIGHT, HADI SUSANTO
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- Journal:
- European Journal of Applied Mathematics / Volume 23 / Issue 2 / April 2012
- Published online by Cambridge University Press:
- 26 August 2011, pp. 201-244
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We consider a Josephson junction system installed with a finite length inhomogeneity, either of micro-resistor or micro-resonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or – for instance by varying the length of the inhomogeneity – may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity – a relation we determine explicitly. In combination with continuation arguments and Sturm–Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, a microresistor has exactly one pinned fluxon, i.e. the system selects one unique pinned stable pinned configuration, and a microresonator has at least one stable pinned configuration. Moreover, it is shown that both for micro-resistors and micro-resonators this stable pinned configuration may be non-monotonic – something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on micro-resonators.
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- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Synthesis and distribution of cytokeratins in healthy and ulcerated bovine claw epidermis
- KAY A. K. HENDRY, AMANDA J. MACCALLUM, CHRISTOPHER H. KNIGHT, COLIN J. WILDE
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- Journal:
- Journal of Dairy Research / Volume 68 / Issue 4 / November 2001
- Published online by Cambridge University Press:
- 16 April 2002, pp. 525-537
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- November 2001
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Keratinization of the epidermal cells of the bovine claw generates the horn that gives the tissue its mechanical strength. Disruption of keratinization is likely to have a detrimental effect on the strength and integrity of the horn, and could lead to solar lesions and lameness. As part of a wider investigation of the cell biological causes of lameness in dairy animals, we have compared keratin synthesis and distribution in healthy bovine claw tissue with those in hooves with solar ulcers. Protein synthesis was measured by [35S]-labelled amino acid incorporation in claw tissue explant cultures. [35S]-labelled protein synthesis was higher in tissue from diseased claws than in healthy claws, and highest at the ulcer site. The identity of proteins synthesised in vitro did not differ between healthy and diseased tissue. DNA synthesis indicative of cell proliferation was also elevated in diseased tissue. Immunoblotting after one- or two-dimensional electrophoresis showed cytokeratins (CK) 4, 5/6, 10 and 14 to be amongst those expressed in healthy claw tissue. The relative abundance of these keratins was not altered in healthy regions of ulcerated hooves, nor at the ulcer site, but CK16, not usually found in healthy tissue, was detected in the sole of diseased claws. CK5/6 and CK14 were shown by immunohistochemistry to be present in the basal epidermis of healthy tissue, whereas CK10 was found in supra-basal layers. In healthy tissue from ulcerated claws, this distribution was unaltered, but at the site of solar ulcers, CK5/6 and CK14 were each found in both basal and supra-basal epidermis. The study suggests that solar ulceration of the bovine claw is not associated with gross alteration in the keratin composition of the tissue, but causes abnormal distribution of cytokeratins, perhaps as a result of loss of positional cues from the basement membrane. Ulceration did, however, stimulate cell repair involving epidermal protein synthesis (including keratins), and keratinocyte proliferation.
Effect of endocrine and paracrine factors on protein synthesis and cell proliferation in bovine hoof tissue culture
- KAY A. K. HENDRY, AMANDA J. MacCALLUM, CHRISTOPHER H. KNIGHT, COLIN J. WILDE
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- Journal of Dairy Research / Volume 66 / Issue 1 / February 1999
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- 01 February 1999, pp. 23-33
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- February 1999
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Laminitis is a major cause of lameness in dairy cattle, and is widely attributed to a defect in the horny tissue that gives the hoof its mechanical strength. Defective horn is associated with, and may be preceded by, impaired keratin deposition in the hoof epidermis. The cause of abnormal keratin deposition is not easily identified but, like epidermal keratinization in other tissues, is likely to be controlled by hormones and the paracrine action of locally produced growth factors. The hormonal regulation of keratin synthesis and cell proliferation in the bovine hoof was studied using tissue explants in organ culture. As the highest incidence of laminitis is in early lactation, the study focused on insulin, cortisol and prolactin, three hormones implicated in lactogenesis and galactopoiesis. Incubation of tissue explants for 24 h in medium containing insulin (10–5000 ng/ml) stimulated protein synthesis measured by incorporation of 35 S-labelled amino acids. Histochemical examination showed that insulin binding co-localized with the site of protein synthesis. Insulin also stimulated DNA synthesis, an index of cell proliferation, which was measured by incorporation of [3H]methyl thymidine. Cortisol (10–5000 ng/ml) decreased protein synthesis, whereas prolactin (10–5000 ng/ml) had no significant effect on protein or DNA synthesis. Epidermal growth factor (10–200 ng/ml), a potent inhibitor of keratinization in other tissues, stimulated protein synthesis compared with untreated controls. Epidermal growth factor binding was located microscopically to the germinal and differentiating epidermal layers. SDS-PAGE and fluorography showed that the population of proteins synthesized in the presence of any hormone or growth factor combination did not differ from that in untreated controls and included the keratins involved in horn deposition. The results show that bovine hoof keratinization is under endocrine and growth factor control, and suggest that systemic changes in lactogenic hormones may act to inhibit keratin deposition.
REVIEW ARTICLE Laminitis in the dairy cow: a cell biological approach
- KAY A. K. HENDRY, AMANDA J. MacCALLUM, CHRISTOPHER H. KNIGHT, COLIN J. WILDE
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- Journal of Dairy Research / Volume 64 / Issue 3 / August 1997
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- 01 August 1997, pp. 475-486
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- August 1997
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Lameness is a major welfare concern in dairy cattle. Estimates of the annual incidence of lameness range from 4 to 30%, and even in well managed herds as many as 15% of animals can be affected (Esselmont, 1990). In addition to the cost in animal suffering, lameness is accompanied by loss of production on a scale comparable, in temperate countries, with that caused by mastitis. Lost production, veterinary charges and milk discard costs coupled with reduced fertility or premature culling in turn make lameness a major economic factor in dairy farming. In the UK alone, the estimated cost in lost production is £44–£90 million per annum, equivalent to £10–20 per cow (Booth, 1989; Esselmont, 1990).