Enhanced transmission through a subwavelength aperture using metamaterials

We report an enhanced transmission through a single circular subwavelength aperture that is incorporated with a split ring resonator (SRR) at the microwave regime. Transmission enhancement factors as high as 530 were observed in the experiments when the SRR was located in front of the aperture in order to efficiently couple the electric field component of the incident electromagnetic wave at SRR's electrical resonance frequency. The experimental results were supported by numerical analyses. The physical origin of the transmission enhancement phenomenon was discussed by examining the induced surface currents on the structures

Chiral metamaterials with negative refractive index based on four "U" split ring resonators

A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive index is realized for circularly polarized waves due to the large chirality. The experimental results are in good agreement with the numerical results.Comment: 4 pages, 4 figures, Published as cover on AP

Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields

En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. Para estos sistemas caracterizamos sus retratos de fase globales en el disco de Poincaré y describimos sus diagramas de bifurcación. Las formas normales de estos sistemas las obtenemos utilizando las formas normales de los sistemas cúbicos homogéneos dados en [1], y añadiendo a estos los términos lineales de manera que el origen sea un centro de tipo lineal o un centro nilpotente. Luego describimos los retratos de fase globales en el disco de Poincaré de estas doce familias de sistemas. Para ello en primer lugar encontramos los retratos de fase en el infinito de esos sistemas, y luego encontramos los retratos de fase locales en los puntos singulares finitos. Usando estos dos resultados determinamos los posibles retratos de fase globales de cada familia. Para algunas familias los puntos singulares finitos son demasiado complicados para estudiar sus retratos de fase local, y en algunos otros casos ni siquiera podemos calcular los puntos singulares finitos. En estas situaciones primero determinamos el número máximo de puntos singulares finitos que los sistemas pueden tener, a continuación utilizando el hecho de que el índice total de todos los puntos singulares de un campo vectorial en la esfera de Poincaré con un número finito de puntos singulares es 2 (este resultado se conoce como el teorema de Poincaré–Hopf) determinamos el número posible de puntos singulares finitos y sus posibles retratos fase locales posibles. Para determinar los posibles retratos de fase globales posibles miramos el número de puntos de una recta que pasa por el origen que se encuentran en el mismo nivel de energía. Puesto que los polinomios Hamiltonianos de las doce familias de sistemas son de cuarto grado, no puede haber más que cuatro de tales puntos. Si encontramos que sólo un retrato de fase global es posible para una familia, entonces este es el retrato de fase de la familia. Si hay más de un retrato de fase global posible, entonces mostramos que podemos elegir los parámetros de forma que los retratos de fase se realicen. Por último, después de haber determinado los retratos de fase global para cada familia, describimos sus diagramas de bifurcación utilizando las dos diferencias principales entre estos retratos de fase: el número de puntos singulares finitos y el número de sillas en el mismo nivel de energía. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448.In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. Moreover we provide the bifurcation diagrams of these differential systems. We obtain the normal forms of these systems using the normal forms of cubic homogeneous systems given in [1], and by adding to them the linear terms such that the origin is a linear type center or a nilpotent center. Then we describe the global phase portraits on the Poincaré disk of these twelve families of systems. To do this we first find the phase portraits at infinity of those systems, and then we find the local phase portraits at the finite singular points. Using these two results we determine the possible global phase portraits of each family. For some families the finite singular points are too complicated to study their local phase portraits, in some other cases we even cannot calculate the finite singular points. In these situations we first determine the maximum number of finite singular points that the systems can have, then using the fact that the total index of all the singular points of a vector field on the Poincaré sphere with a finite number of singular points is 2 (this result is known as the Poincaré–Hopf theorem) we determine the possible number of finite singular points and their possible local phase portraits. To determine the possible global phase portraits we look at the number of points of a straight line passing through the origin that are at the same energy level. Since the Hamiltonian polynomials of the twelve families of systems are quartic, there can be at most four such points. If we find only one possible global phase portrait for a family then we are done. If there are more than one possible global phase portrait then we show that for some specific choice of parameters those phase portraits are indeed realizable. Finally, after having determined the global phase portraits for each fam- ily, we describe their bifurcation diagrams using the two main differences between these phase portraits: the number of finite singular points and the number of saddles at the same energy level. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448

Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields

En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. Para estos sistemas caracterizamos sus retratos de fase globales en el disco de Poincaré y describimos sus diagramas de bifurcación. Las formas normales de estos sistemas las obtenemos utilizando las formas normales de los sistemas cúbicos homogéneos dados en [1], y añadiendo a estos los términos lineales de manera que el origen sea un centro de tipo lineal o un centro nilpotente. Luego describimos los retratos de fase globales en el disco de Poincaré de estas doce familias de sistemas. Para ello en primer lugar encontramos los retratos de fase en el infinito de esos sistemas, y luego encontramos los retratos de fase locales en los puntos singulares finitos. Usando estos dos resultados determinamos los posibles retratos de fase globales de cada familia. Para algunas familias los puntos singulares finitos son demasiado complicados para estudiar sus retratos de fase local, y en algunos otros casos ni siquiera podemos calcular los puntos singulares finitos. En estas situaciones primero determinamos el número máximo de puntos singulares finitos que los sistemas pueden tener, a continuación utilizando el hecho de que el índice total de todos los puntos singulares de un campo vectorial en la esfera de Poincaré con un número finito de puntos singulares es 2 (este resultado se conoce como el teorema de Poincaré-Hopf) determinamos el número posible de puntos singulares finitos y sus posibles retratos fase locales posibles. Para determinar los posibles retratos de fase globales posibles miramos el número de puntos de una recta que pasa por el origen que se encuentran en el mismo nivel de energía. Puesto que los polinomios Hamiltonianos de las doce familias de sistemas son de cuarto grado, no puede haber más que cuatro de tales puntos. Si encontramos que sólo un retrato de fase global es posible para una familia, entonces este es el retrato de fase de la familia. Si hay más de un retrato de fase global posible, entonces mostramos que podemos elegir los parámetros de forma que los retratos de fase se realicen. Por último, después de haber determinado los retratos de fase global para cada familia, describimos sus diagramas de bifurcación utilizando las dos diferencias principales entre estos retratos de fase: el número de puntos singulares finitos y el número de sillas en el mismo nivel de energía. [1] A. Cima and J. Llibre, "Algebraic and topological classification of the homogeneous cubic vector fields in the plane", J. Math. Anal. and Appl. 147 (1990), 420-448.In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. Moreover we provide the bifurcation diagrams of these differential systems. We obtain the normal forms of these systems using the normal forms of cubic homogeneous systems given in [1], and by adding to them the linear terms such that the origin is a linear type center or a nilpotent center. Then we describe the global phase portraits on the Poincaré disk of these twelve families of systems. To do this we first find the phase portraits at infinity of those systems, and then we find the local phase portraits at the finite singular points. Using these two results we determine the possible global phase portraits of each family. For some families the finite singular points are too complicated to study their local phase portraits, in some other cases we even cannot calculate the finite singular points. In these situations we first determine the maximum number of finite singular points that the systems can have, then using the fact that the total index of all the singular points of a vector field on the Poincaré sphere with a finite number of singular points is 2 (this result is known as the Poincaré-Hopf theorem) we determine the possible number of finite singular points and their possible local phase portraits. To determine the possible global phase portraits we look at the number of points of a straight line passing through the origin that are at the same energy level. Since the Hamiltonian polynomials of the twelve families of systems are quartic, there can be at most four such points. If we find only one possible global phase portrait for a family then we are done. If there are more than one possible global phase portrait then we show that for some specific choice of parameters those phase portraits are indeed realizable. Finally, after having determined the global phase portraits for each fam- ily, we describe their bifurcation diagrams using the two main differences between these phase portraits: the number of finite singular points and the number of saddles at the same energy level. [1] A. Cima and J. Llibre, "Algebraic and topological classification of the homogeneous cubic vector fields in the plane", J. Math. Anal. and Appl. 147 (1990), 420-448

The role of T2-weighted images in assessing the grade of extraprostatic extension of the prostate carcinoma

Purpose Extraprostatic extension (EPE) is an unfavorable prognostic factor and the grade of EPE is also shown to be correlated with the prognosis of prostate cancer. The current study assessed the value of prostate magnetic resonance imaging (MRI) in measuring the radial distance (RD) of EPE and the role of T2 WI signs in predicting the grade of EPE. Materials and methods A total of 110 patients who underwent prostate MRI before radical prostatectomy are enrolled in this retrospective study. Eighty-four patients have organ confined disease and the remaining twenty-six patients have EPE all verified by histopathology. Prostate MRI examinations were conducted with 3T MRI scanner and phased array coil with the following sequences: T2 WI, T1 WI, DCE, DWI with ADC mapping, and high b-value at b = 1500 s/mm(2). The likelihood of EPE with 5-point Likert scale was assigned, several MRI features were extracted for each dominant tumor identified by using T2 WI. Tumors with Likert scales 4-5 were evaluated further to obtain MRI-based RD. The relationship between pathological and MRI-determined RD was tested. Univariate and multivariate logistic regression models were developed to detect the grade of pathological EPE. The inputs were among the 2 clinical parameters and 4 MRI features. Results There is a moderate correlation between pathological RD and MRI-determined RD (rho = 0.45, P < 0.01). In univariate and multivariate models, MRI features and clinical parameters possess varying significance levels (univariate models; P = 0.048-0.788, multivariate models; P = 0.173-0.769). Multivariate models perform better than the univariate models by offering fair to good performances (AUC = 0.69-0.85). The multivariate model that employs the MRI features offers better performance than the model employs clinical parameters (AUC = 0.81 versus 0.69). Conclusion Co-existence of T2 WI signs provide higher diagnostic value even than clinical parameters in predicting the grade of EPE. Combined use of clinical parameters and MRI features deliver slightly superior performance than MRI features alone