1,721,192 research outputs found
On a bifurcation problem arising in cholesteric liquid crystal theory
No full textIn a cholesteric liquid crystal the director field n(x, y, z) tends to form a right-angle helicoid around a twist axis in order to minimize the internal e- nergy; however, a fixed alignment of the director field at the boundary (strong anchoring) can give rise to distorted configurations of the director field, as oblique helicoid, in order to save energy. The transition to this distorted configurations depend on the boundary conditions and on the geometry of the liquid crystal, and it is known as Freedericksz transition (without external fields). We consider the classical situation of a thin layer between two glass sheet as- suming the Oseen-Frank model for the energy, and that the director field depend only on the direction z orthogonal to the layer; then we focus on two kinds of boundary conditions: the planar case and the orthogonal case. In the first, we impose that n(0) = (1, 0, 0), n(d) = (cos α, sin α, 0) (where z = 0 and z = d > 0 are, respectively, the bottom and the top of the layer), and search for the couples (d, α) such that oblique helicoid appear. In the case K1 > 0, K2 = K3 = 1 for the elastic constants of the Oseen-Frank energy, we completely characterize these couples. In the second case it is a classical result that oblique helicoid bifurcates from the trivial solution n(z) = (0, 0, 1) for suitable values of d; then we study the exact number of these nontrivial solutions and their stability
On the cubic and cubic-quintic optical vortices equations
No full textAn optical vortex can appear when a light beam with nonzero angular momentum propagates in a suitable nonlinear medium. In some situations has been observed that the light intensity vanish at the center of the vortex (where the phase of the electromagnetic field is undefined), while the light beam assumes a ring-shaped structure. In this paper we consider two classical cases in which such kind of phenomena occur: the case of the self focusing cubic nonlinearity, and the case of competing quintic and cubic nonlinearity. In both cases we study the nonlinear Schrödinger equation of the optical field (with various boundary conditions) by means of min-max methods, and we prove the existence of saddle point type solutions, as well as minimum type solutions
Uniqueness of director configuration states for liquid crystals in the case of weak anchoring
No full textIn a thin layer of liquid crystal the configuration of the director field depends on the interaction between
the elastic properties of the material, the thickness d of the layer, the boundary conditions and the external
fields that may have been applied. Suitable combinations of these factors can give rise to distorted
configurations (Freedericksz transitions). In this paper we assume the Oseen-Frank model for the energy
and that the director field depends only on the direction orthogonal to the layer; we assume also weak
anchoring conditions at the two bounding surfaces, and we mainly study the problem of uniqueness of
such distorted configurations. More precisely, we first consider the nematic case in the presence of a
magnetic field H, and we prove the uniqueness of the stable configuration provided the magnitude of H is
between two critical thresholds, simplifying some results already known in the literature, and calculating
explicitly the critical thresholds. Then we study the case of a cholesteric liquid crystal without external
field. In this case the director field tends to form a right-angle helicoid around a twist axis orthogonal to
the layer, and we have distorted configurations (namely oblique helicoid) for suitable value of d. Also in
this case, with suitable restrictions on the elastic constants in the Oseen-Frank energy, we find two critical
thresholds for d, and we prove the existence of only one stable director configuration if d is between them
Hypofractionated stereotactic radiotherapy in the treatment of NSCLC in inoperable stage
No full textRemarks on periodic solutions of second order hamiltonian systems in a unbounded potential well
No full textParticle therapy in prostate cancer: a review
No full textWhile dose escalation is proving important to achieve satisfactory long-term outcomes in prostate cancer, the optimal radiation modality to deliver the treatment is still a topic of debate. Charged particle beams can offer improved dose distributions to the target volume as compared to conventional 3D-conformal radiotherapy, with better sparing of surrounding healthy tissues. Exquisite dose distributions, with the fulfillment of dose-volume constraints to normal tissues, however, can also be achieved with photon-based intensity-modulated techniques. This review summarizes the literature on the use of particle therapy in prostate cancer and attempts to put in perspective its relative merits compared to current photon-based radiotherapy
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