Differential equations with soliton behaviour

Various non-linear wave equations are found to possess solitons - stable solitary waves which only undergo a change of position on collision with each other. It is shown in chapter 1, how the various soliton properties of the sine-Gordon equation, u(_xy) = F(u) sin u, May be derived from its Backlund Transformation. Most of the rest of the thesis consists of several attempts to find Backlund Transformations for other equations of the form u = F(u) by generalizing the usual form of the Backlund Transformation. The only exception to this is in chapter 2 where equations of the form u(_xy) = A(x,y,u).u(_x) + B(x,y,u).u(_y) + C(x,y,u) are considered. The rest of chapter 2 considers the effect of allowing the Backlund Transformation to depend explicitly on the independent variables or on integrals of the dependent variables. The rest of this thesis concentrates on allowing the Backlund Transformation to depend on derivatives only of the "old" and "new" variables, u and u'. It is found that if u and u' satisfy u(_xy) = F(u) where F'''(u) = K.F''(u) and F''(u) = K.F(u) then there are no Backlund Transformations of the following form. Chapter 3. u’(_x) = P(u,u';p(_1),.., ,P(_N);q(_1),...,q(M)) u;(_y)= Q(u,u';p(_1),...,P(_N);q(_1),...,q(_M)) except possibly when M = 1 , N > 7 and F(u) = A(_1).e(^cu) + A(_2).e(^-2cu). Chapter 4. u’(_xx) = P(u, u’, u(_x), u’(_x), x(_y), u(_xx), u(_yy) u’(_y) = Q(u, u’, u(_x), u’(_x), x(_y), u(_xx), u(_yy) Chapter 5 (^1)/(_2) (p’(_N+1) p(_N+1) – P(P(_0), P(_1),…,P(_N);P’(_0),…,P’(_N) N <5 (^1)/(_2)(q’ +q) = Q(P(_0), P(_1),…,P(_N);P(_0),…,P’(_N

Experimental evidence of intrabeam scattering in a free-electron laser driver

Abstract The effect of multiple small-angle Coulomb scattering, or intrabeam scattering (IBS) is routinely observed in electron storage rings over the typical damping time scale of milliseconds. So far, IBS has not been observed in single pass electron accelerators because charge density orders of magnitude higher than in storage rings would be needed. We show that such density is now available at high brightness electron linacs for free-electron lasers (FELs). We report measurements of the beam energy spread in the FERMI linac in the presence of the microbunching instability, which are consistent with a revisited IBS model for single pass systems. We also show that neglecting the hereby demonstrated effect of IBS in the parameter range typical of seeded VUV and soft x-ray FELs, results in too conservative a facility design, or failure to realise the accessible potential performance. As an example, an optimization of the FERMI parameters driven by an experimentally benchmarked model, opens the door to the extension of stable single spectral line emission to the water window (2.3–4.4 nm), with far-reaching implications for experiments in a variety of disciplines, ranging from physics and chemistry to biology and material sciences, and including nonlinear x-ray optics based on the four-wave-mixing approach.</jats:p

Microbunching instability characterization via temporally modulated laser pulses

High-brightness electron bunches, such as those generated and accelerated in free-electron lasers (FELs), can develop small-scale structure in the longitudinal phase space. This causes variations in the slice energy spread and current profile of the bunch which then undergo amplification, in an effect known as the microbunching instability. By imposing energy spread modulations on the bunch in the low-energy section of an accelerator, using an undulator and a modulated laser pulse in the center of a dispersive chicane, it is possible to manipulate the bunch longitudinal phase space. This allows for the control and study of the instability in unprecedented detail. We report measurements and analysis of such modulated electron bunches in the 2D spectrotemporal domain at the Fermi FEL, for three different bunch compression schemes. We also perform corresponding simulations of these experiments and show that the codes are indeed able to reproduce the measurements across a wide spectral range. This detailed experimental verification of the ability of codes to capture the essential beam dynamics of the microbunching instability will benefit the design and performance of future FELs

Microbunching instability characterization via temporally modulated laser pulses

High-brightness electron bunches, such as those generated and accelerated in free-electron lasers (FELs), can develop small-scale structure in the longitudinal phase space. This causes variations in the slice energy spread and current profile of the bunch which then undergo amplification, in an effect known as the microbunching instability. By imposing energy spread modulations on the bunch in the low-energy section of an accelerator, using an undulator and a modulated laser pulse in the centre of a dispersive chicane, it is possible tomanipulate the bunch longitudinal phase space. This allows for the control and study of the instability in unprecedented detail. We report measurements and analysis of such modulated electron bunches in the 2Dspectro-temporal domain at the FERMI FEL, for three different bunch compression schemes. We also perform corresponding simulations of these experiments and show that the codes are indeed able to reproduce the measurements across a wide spectral range. This detailed experimental verification of the ability of codes to capture the essential beam dynamics of the microbunching instability will benefit the design and performance of future FELs

Specification and design for Full Energy Beam Exploitation of the Compact Linear Accelerator for Research and Applications

The Compact Linear Accelerator for Research and Applications (CLARA) is a 250 MeV ultrabright electron beam test facility at STFC Daresbury Laboratory. A user beam line has been designed to maximise exploitation of CLARA in a variety of fields, including novel acceleration and new modalities of radiotherapy. In this paper we present the specification and design of this beam line for Full Energy Beam Exploitation (FEBE). We outline the key elements which provide users to access ultrashort, low emittance electron bunches in two large experiment chambers. The results of start-to-end simulations are reported which verify the expected beam parameters delivered to these chambers. Key technical systems are detailed, including those which facilitate combination of electron bunches with high power laser pulses.Comment: 13 pages, 12 figure

Quality of life, psychological morbidity and family stress in elderly residing in the community

Este estudo procurou investigar as relações existentes entre morbilidade psicológica, stress familiar e qualidade de vida (QV) da pessoa idosa. A amostra foi constituída por 126 idosos. Os instrumentos utilizados foram: The Lawton Instrumental Activities of Daily Living (IADL), Quality of Life (WHOQOL-Bref), Geriatric Anxiety Inventory (GSI), Geriatric Depression Scale (GDS); e Index of Family Relations (IFR). Os resultados revelaram a importância da idade, estado civil, escolaridade e número de patologias assim como o género na capacidade funcional, morbilidade, stress familiar e QV. Ao nível dos preditores, a depressão foi a variável que mais contribuiu para a QV. Não foram encontradas variáveis moderadoras no modelo. A discussão e implicações dos resultados são abordadas bem como a intervenção psicológica nesta população.This study sought to understand the relationships among psychological morbidity, family stress and quality of life (QL) of elderly. The sample consisted of 126 elderly. The following instruments were used: the Lawton Instrumental Activities of Daily Living (IADL); Quality of Life (WHOQOL-Bref), Geriatric Anxiety Inventory (GSI), Geriatric Depression Scale (GDS), and the Index of Family Relations (IFR). Results revealed the importance of age, marital status, education and number of pathologies as well as gender on functional capacity, morbidity, family stress and QV. In terms of predictors, depression was the variable that contributed the most to QL. There were no moderating variables in the model. Discussion and implications of results are addressed as well as psychological interventions.(undefined

Discretization Provides a Conceptually Simple Tool to Build Expression Networks

Biomarker identification, using network methods, depends on finding regular co-expression patterns; the overall connectivity is of greater importance than any single relationship. A second requirement is a simple algorithm for ranking patients on how relevant a gene-set is. For both of these requirements discretized data helps to first identify gene cliques, and then to stratify patients

Systemic mastocytosis associated with t(8;21)(q22;q22) acute myeloid leukemia

Although KIT mutations are present in 20–25% of cases of t(8;21)(q22;q22) acute myeloid leukemia (AML), concurrent development of systemic mastocytosis (SM) is exceedingly rare. We examined the clinicopathologic features of SM associated with t(8;21)(q22;q22) AML in ten patients (six from our institutions and four from published literature) with t(8;21) AML and SM. In the majority of these cases, a definitive diagnosis of SM was made after chemotherapy, when the mast cell infiltrates were prominent. Deletion 9q was an additional cytogenetic abnormality in four cases. Four of the ten patients failed to achieve remission after standard chemotherapy and seven of the ten patients have died of AML. In the two patients who achieved durable remission after allogeneic hematopoietic stem cell transplant, recipient-derived neoplastic bone marrow mast cells persisted despite leukemic remission. SM associated with t(8;21) AML carries a dismal prognosis; therefore, detection of concurrent SM at diagnosis of t(8;21) AML has important prognostic implications