895 resultados para Non-commutative Landau problem
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In university studies, it is not unusual for students to drop some of the subjects they have enrolled in for the academic year. They start by not attending lectures, sometimes due to neglect or carelessness, or because they find the subject too difficult, this means that they lose the continuity in the topics that the professor follows. If they try to attend again they discover that they hardly understand anything and become discouraged and so decide to give up attending lectures and study on their own. However some fail to turn up to do their final exams and the failure rate of those who actually do the exams is high. The problem is that this is not only the case with one specific subject, but it is often the same with many subjects. The result is that students arent’s productive enough, wasting time and also prolonging their years of study which entails a great cost for families. Degree courses structured to be conducted and completed in three academic courses, it may in fact take up to an average of six or more academic courses. In this paper, we have studied this problem, which apart from the waste of money and time, produces frustration in the student, who finds that he has not been able to achieve what he had proposed at the beginning of the course. It is quite common, to find students who do not even pass nor 50% of the subjects they had enrolled in for the academic year. If this happens repeatedly to a student, it can be the point when he considers dropping out altogether. This is also a concern for the universities, especially in the early courses. In our experience as professors, we have found that students, who attend lectures regularly and follow the explanations, approach the final exams with confidence and rarely fail the subject. In this proposal we present some techniques and methods carried out to solve in possible, the problem of lack of attendance to lectures. This involves "rewarding students for their assistance and participation in lectures". Rewarding assistance with a "prize" that counts for the final mark on the subject and involving more participation in the development of lectures. We believe that we have to teach students to use the lectures as part of their learning in a non-passive way. We consider the professor's work as fundamental in terms of how to convey the usefulness of these topics explained and the applications that they will have for their professional life in the future. In this way the student see for himself the use and importance of what he is learning. When his participation is required, he will feel more involved and confident participating in the educational system. Finally we present statistical results of studies carried out on different degrees and on different subjects over two consecutive years. In the first year we assessed only the final exams without considering the students attendance, or participation. In the second year, we have applied the techniques and methods proposed here. In addition we have compared the two ways of assessing subjects.
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We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.
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Aims Agricultural soils in semiarid Mediterranean areas are characterized by low organic matter contents and low fertility levels. Application of crop residues and/or manures as amendments is a cost-effective and sustainable alternative to overcome this problem. However, these management practices may induce important changes in the nitrogen oxide emissions from these agroecosystems, with additional impacts on carbon dioxide emissions. In this context, a field experiment was carried out with a barley (Hordeum vulgare L.) crop under Mediterranean conditions to evaluate the effect of combining maize (Zea mays L.) residues and N fertilizer inputs (organic and/or mineral) on these emissions. Methods Crop yield and N uptake, soil mineral N concentrations, dissolved organic carbon (DOC), denitrification capacity, N2O, NO and CO2 fluxes were measured during the growing season. Results The incorporation of maize stover increased N2O emissions during the experimental period by c. 105 %. Conversely, NO emissions were significantly reduced in the plots amended with crop residues. The partial substitution of urea by pig slurry reduced net N2O emissions by 46 and 39 %, with and without the incorporation of crop residues respectively. Net emissions of NO were reduced 38 and 17 % for the same treatments. Molar DOC:NO 3 − ratio was found to be a robust predictor of N2O and NO fluxes. Conclusions The main effect of the interaction between crop residue and N fertilizer application occurred in the medium term (4–6 month after application), enhancing N2O emissions and decreasing NO emissions as consequence of residue incorporation. The substitution of urea by pig slurry can be considered a good management strategy since N2O and NO emissions were reduced by the use of the organic residue.
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En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.
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The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.
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This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.
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In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem
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Non-linear behavior of soils during a seismic event has a predominant role in current site response analysis. Soil response analysis consistently indicates that the stress-strain relationship of soils is nonlinear and shows hysteresis. When focusing in forced response simulations, time integrations based on modal analysis are widely considered, however parametric analysis, non-linear behavior and complex damping functions make difficult the online use of standard discretization strategies, e.g. those based on the use of finite element. In this paper we propose a new harmonic analysis formulation, able to address forced response simulation of soils exhibiting their characteristic nonlinear behavior. The solution can be evaluated in real-time from the offline construction of a parametric solution of the associated linearized problem within the Proper Generalized Decomposition framework.
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El estudio sísmico en los últimos 50 años y el análisis del comportamiento dinámico del suelo revelan que el comportamiento del suelo es altamente no lineal e histéretico incluso para pequeñas deformaciones. El comportamiento no lineal del suelo durante un evento sísmico tiene un papel predominante en el análisis de la respuesta de sitio. Los análisis unidimensionales de la respuesta sísmica del suelo son a menudo realizados utilizando procedimientos lineales equivalentes, que requieren generalmente pocos parámetros conocidos. Los análisis de respuesta de sitio no lineal tienen el potencial para simular con mayor precisión el comportamiento del suelo, pero su aplicación en la práctica se ha visto limitada debido a la selección de parámetros poco documentadas y poco claras, así como una inadecuada documentación de los beneficios del modelado no lineal en relación al modelado lineal equivalente. En el análisis del suelo, el comportamiento del suelo es aproximado como un sólido Kelvin-Voigt con un módulo de corte elástico y amortiguamiento viscoso. En el análisis lineal y no lineal del suelo se están considerando geometrías y modelos reológicos más complejos. El primero está siendo dirigido por considerar parametrizaciones más ricas del comportamiento linealizado y el segundo mediante el uso de multi-modo de los elementos de resorte-amortiguador con un eventual amortiguador fraccional. El uso del cálculo fraccional está motivado en gran parte por el hecho de que se requieren menos parámetros para lograr la aproximación exacta a los datos experimentales. Basándose en el modelo de Kelvin-Voigt, la viscoelasticidad es revisada desde su formulación más estándar a algunas descripciones más avanzada que implica la amortiguación dependiente de la frecuencia (o viscosidad), analizando los efectos de considerar derivados fraccionarios para representar esas contribuciones viscosas. Vamos a demostrar que tal elección se traduce en modelos más ricos que pueden adaptarse a diferentes limitaciones relacionadas con la potencia disipada, amplitud de la respuesta y el ángulo de fase. Por otra parte, el uso de derivados fraccionarios permite acomodar en paralelo, dentro de un análogo de Kelvin-Voigt generalizado, muchos amortiguadores que contribuyen a aumentar la flexibilidad del modelado para la descripción de los resultados experimentales. Obviamente estos modelos ricos implican muchos parámetros, los asociados con el comportamiento y los relacionados con los derivados fraccionarios. El análisis paramétrico de estos modelos requiere técnicas numéricas eficientemente capaces de simular comportamientos complejos. El método de la Descomposición Propia Generalizada (PGD) es el candidato perfecto para la construcción de este tipo de soluciones paramétricas. Podemos calcular off-line la solución paramétrica para el depósito de suelo, para todos los parámetros del modelo, tan pronto como tales soluciones paramétricas están disponibles, el problema puede ser resuelto en tiempo real, porque no se necesita ningún nuevo cálculo, el solucionador sólo necesita particularizar on-line la solución paramétrica calculada off-line, que aliviará significativamente el procedimiento de solución. En el marco de la PGD, parámetros de los materiales y los diferentes poderes de derivación podrían introducirse como extra-coordenadas en el procedimiento de solución. El cálculo fraccional y el nuevo método de reducción modelo llamado Descomposición Propia Generalizada han sido aplicado en esta tesis tanto al análisis lineal como al análisis no lineal de la respuesta del suelo utilizando un método lineal equivalente. ABSTRACT Studies of earthquakes over the last 50 years and the examination of dynamic soil behavior reveal that soil behavior is highly nonlinear and hysteretic even at small strains. Nonlinear behavior of soils during a seismic event has a predominant role in current site response analysis. One-dimensional seismic ground response analysis are often performed using equivalent-linear procedures, which require few, generally well-known parameters. Nonlinear analyses have the potential to more accurately simulate soil behavior, but their implementation in practice has been limited because of poorly documented and unclear parameter selection, as well as inadequate documentation of the benefits of nonlinear modeling relative to equivalent linear modeling. In soil analysis, soil behaviour is approximated as a Kelvin-Voigt solid with a elastic shear modulus and viscous damping. In linear and nonlinear analysis more complex geometries and more complex rheological models are being considered. The first is being addressed by considering richer parametrizations of the linearized behavior and the second by using multi-mode spring-dashpot elements with eventual fractional damping. The use of fractional calculus is motivated in large part by the fact that fewer parameters are required to achieve accurate approximation of experimental data. Based in Kelvin-Voigt model the viscoelastodynamics is revisited from its most standard formulation to some more advanced description involving frequency-dependent damping (or viscosity), analyzing the effects of considering fractional derivatives for representing such viscous contributions. We will prove that such a choice results in richer models that can accommodate different constraints related to the dissipated power, response amplitude and phase angle. Moreover, the use of fractional derivatives allows to accommodate in parallel, within a generalized Kelvin-Voigt analog, many dashpots that contribute to increase the modeling flexibility for describing experimental findings. Obviously these rich models involve many parameters, the ones associated with the behavior and the ones related to the fractional derivatives. The parametric analysis of all these models require efficient numerical techniques able to simulate complex behaviors. The Proper Generalized Decomposition (PGD) is the perfect candidate for producing such kind of parametric solutions. We can compute off-line the parametric solution for the soil deposit, for all parameter of the model, as soon as such parametric solutions are available, the problem can be solved in real time because no new calculation is needed, the solver only needs particularize on-line the parametric solution calculated off-line, which will alleviate significantly the solution procedure. Within the PGD framework material parameters and the different derivation powers could be introduced as extra-coordinates in the solution procedure. Fractional calculus and the new model reduction method called Proper Generalized Decomposition has been applied in this thesis to the linear analysis and nonlinear soil response analysis using a equivalent linear method.
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The Department of Structural Analysis of the University of Santander has been for a longtime involved in the solution of the country´s practical engineering problems. Some of these have required the use of non-conventional methods of analysis, in order to achieve adequate engineering answers. As an example of the increasing application of non-linear computer codes in the nowadays engineering practice, some cases will be briefly presented. In each case, only the main features of the problem involved and the solution used to solve it will be shown
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Non-suicidal self-injury (NSSI), such as cutting and burning, is a widespread social problem among lesbian, gay, bisexual, transgender, queer, and questioning (LGBTQ) youth. Extant research indicates that this population is more than twice as likely to engage in NSSI than heterosexual and cisgender (non-transgender) youth. Despite the scope of this social problem, it remains relatively unexamined in the literature. Research on other risk behaviors among LGBTQ youth indicates that experiencing homophobia and transphobia in key social contexts such as families, schools, and peer relationships contributes to health disparities among this group. Consequently, the aims of this study were to examine: (1) the relationship between LGBTQ youth's social environments and their NSSI behavior, and (2) whether/how specific aspects of the social environment contribute to an understanding of NSSI among LGBTQ youth. This study was conducted using an exploratory, sequential mixed methods design with two phases. The first phase of the study involved analysis of transcripts from interviews conducted with 44 LGBTQ youth recruited from a community-based organization. In this phase, five qualitative themes were identified: (1) Violence; (2) Misconceptions, Stigma, and Shame; (3) Negotiating LGBTQ Identity; (4) Invisibility and Isolation; and (5) Peer Relationships. Results from the qualitative phase were used to identify key variables and specify statistical models in the second, quantitative, phase of the study, using secondary data from a survey of 252 LGBTQ youth. The qualitative phase revealed how LGBTQ youth, themselves, described the role of the social environment in their NSSI behavior, while the quantitative phase was used to determine whether the qualitative findings could be used to predict engagement in NSSI among a larger sample of LGBTQ youth. The quantitative analyses found that certain social-environmental factors such as experiencing physical abuse at home, feeling unsafe at school, and greater openness about sexual orientation significantly predicted the likelihood of engaging in NSSI among LGBTQ youth. Furthermore, depression partially mediated the relationships between family physical abuse and NSSI and feeling unsafe at school and NSSI. The qualitative and quantitative results were compared in the interpretation phase to explore areas of convergence and incongruence. Overall, this study's findings indicate that social-environmental factors are salient to understanding NSSI among LGBTQ youth. The particular social contexts in which LGBTQ youth live significantly influence their engagement in this risk behavior. These findings can inform the development of culturally relevant NSSI interventions that address the social realities of LGBTQ youth's lives.
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The last two decades have been marked by a growing public awareness of family violence. Research by social scientists has suggested that family violence is widespread (Gelles and Straus, 1988). It is estimated that every year 1.8 to 4 million women are physically abused by their partners (Novello, 1992). In fact, more women are abused by their husbands or boyfriends than are injured in car accidents, muggings, or rapes (Jaffe, Wolfe, and Wilson, 1990). A recent prevalence study by Fantuzzo, Boruch, Beriama, Atkins, and Marcus (1997) found that children were disproportionately present in households where there was a substantial incident of adult female assault. Experts estimate that 3.3 to 10 million children are exposed to marital violence each year (Carlson, 1984; Straus, 1991). Until recently, most researchers did not consider the impact of parental conflict on the children who witness this violence. The early literature in this field primarily focused on the incidence of violence against women and the inadequate response of community agencies (Jaffe et al, 1990). The needs of children were rarely considered. However, researchers have become increasingly aware that children exposed to marital violence are victims of a range of psychological maltreatment (e.g., terrorizing, isolation;Hart, Brassared & Karlson, 1996) and are at serious risk for the development of psychological problems (Fantuzzo, DePaola, Lambert, Martino, Anderson, and Sutton, 1991). Jouriles, Murphy and O'Leary (1989) found that children of battered women were four times more likely to exhibit psychopathology as were children living in non-violent homes. Further, researchers have found associations between childhood exposure to parental violence and the expression of violence in adulthood (Carlson, 1990). Existing research suggests that children who have witnessed marital violence manifest numerous emotional, social, and behavioral problems (Sternberg et al., 1993; Fantuzzo et al., 1991; Jaffe et al, 1990). Studies have found that children of battered women exhibit more internalizing and externalizing behavior problems than non-witnesschildren (Hughes and Fantuzzo, 1994; McCloskey, Figueredo, and Koss, 1995). In addition, children exposed to marital violence have been found to exhibit difficulties with social problem-solving, and have lower levels of social competence than nonwitnesses (Rosenberg, 1987; Moore, Pepler, Weinberg, Hammond, Waddell, & Weiser, 1990). Other reported difficulties include low self esteem (Hughes, 1988), poor school performance (Moore et al., 1990) and problems with aggression (Holden & Ritchie, 1991; Jaffe, Wolfe, Wilson, & Zak, 1986). Further, within the last decade, researchers have found that some children are traumatized by the witnessing experience, showing elevated levels of posttraumatic stress symptoms (Devoe & Graham-Bermann, 1997; Rossman, Bingham, & Emde, 1996; Kilpatrick, Litt, & Williams, 1997). These findings corroborate clinical reports that describe many exposed children as experiencing trauma reactions. It appears that the negative effects of witnessing marital violence are numerous and varied, ranging from mild emotional and behavioral problems to clinically significant levels of posttraumatic stress symptoms. These incidence figures and research findings indicate that children's exposure to violence is a significant problem in our nation today and has serious implications for the future.
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Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.
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In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.
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Background. Low back pain is an increasing global health problem, which is associated with intervertebral disc (IVD) damage and degeneration. Major changes occur in the nucleus pulposus (NP), with the degradation of the extracellular matrix (ECM).1 Further studies showed that growth factors from transforming growth factor β (TGFβ) and bone morphogenic proteins (BMP) family may induce chondrogenic differentiation of mesenchymal stem cells (MSC).2 Focusing on non-viral gene therapies and their possible translation into the clinics, we investigated if GDF6 (syn. BMP13 or CDMP2) can induce regeneration of degraded NP. We hypothesized that IVD transfected with plasmid over-expressing GDF6 also up-regulates other NP- and chondrogenic cell markers and enhances ECM deposition. Methods. Bovine nucleus pulposus (bNPC) and annulus fibrosus cells (bAFC) were harvested from bovine coccygeal IVD. Primary cells were then electroporized with plasmid GDF6 (Origene, vector RG211366) by optimizing parameters using the Neon Transfection system (Life Technologies, Basel). After transfection, cells were cultured in 2D monolayer or 3D alginate beads for 7, 14 or 21 days. Transfection efficiency of pGDF6 was analyzed by immunohistochemistry and fluorescent microscopy. Cell phenotype was quantified by real-time RT-PCR. To test a non-viral gene therapy applied directly to 3D whole organ culture, coccygeal bovine IVDs were harvested as previously described. Bovine IVDs were transfected by injection of plasmid GDF6 into the center. Electroporation was performed with ECM830 Square Wave Electroporation System (Harvard Apparatus, MA) using 2-needle array electrode or tweezertrodes. 72 h after tranfection discs were fixed and cryosectioned and analyzed by immunofluorescence against GDF6. Results. RT-PCR and immunohistochemistry confirmed up-regulation of GFP and GDF6 in the primary bNPC/bAFC culture. The GFP-tagged GDF6 protein, however, was not visible, possibly due to failure of dimer formation as a result of fusion structure. Organ IVD culture transfection revealed GDF6 positive staining in the center of the disc using 2-needle array electrode. Results from tweezertrodes did not show any GDF6 positive cells. Conclusion. Non-viral transfection is an appealing approach for gene therapy as it fulfills the translational safety aspects of transiency and lacks the toxic effects of viral transduction. We identified novel parameters to successfully transfect primary bovine IVD cells. For transfection of whole IVD explants electroporation parameters need to be further optimized. Acknowledgements. This project was funded by the Lindenhof Foundation (Funds “Research & Teaching”) Project no. 13-02-F. The imaging part of this study was performed with the facility of the Microscopy Imaging Center (MIC), University of Bern. References. Roughly PJ (2004): Spine (Phila), 29:2691-2699 Clarke LE, McConell JC, Sherratt MJ, Derby B, Richardson SM, Hoyland JA (2014), Arthritis Research & Therapy, 16:R67