Measuring the translational and rotational velocity of particles in helical motion using structured light

We measure the rotational and translational velocity components of particles moving in helical motion using the frequency shift they induced to the structured light beam illuminating them. Under Laguerre-Gaussian mode illumination, a particle with a helical motion reflects light that acquires an additional frequency shift proportional to the angular velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.Comment: 5 pages,5 figure

Direction-sensitive transverse velocity measurement by phase-modulated structured light beams

The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge since detection is usually done by means of an interferometric setup which only provides an absolute value of the frequency shift. Here, we put forward a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating micro-particles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.Comment: 5 pages, 4 figure

Searching for the G516T Polymorphism on the CYP2B6 gene in HIV-1Patients

Poster presented at the International Young Researchers in Life Sciences Conference. Pasteur Institute, Paris, France, 26-28 May 2014

Reversed-phase chromatographic separation and downstream precipitation of lupane- and oleanane-type triterpenoids: experiments and modeling based on the method of moments

The reversed-phase chromatographic separation of two triterpenic acids (TTAs), betulinic and oleanolic acids, using a triacontyl (C30) stationary phase was addressed in this work. Methanol, water, acetonitrile, ethanol, isopropanol, ethyl acetate, acetone and mixtures thereof were tested, and the best mobile phase to conduct the separation was found to be methanol/acetonitrile 50/50 (%, v/v) at 23 °C, taking into account parameters like selectivity, resolution and TTAs solubility. The method of moments was used to determine the equilibrium constants of isotherms, the axial dispersion coefficients and the global linear driving force coefficients of pure betulinic and pure oleanolic acids. These parameters were then successfully validated by modeling unary and binary breakthrough curves. Simulated moving bed calculations showed that betulinic and oleanolic acids can be both obtained with purity of 99.2 % and productivity of 56.2 kg/(m3adsorbent day) using the packing material of an Acclaim C30 column with a 1-1-1-1 configuration with columns of 7.5 cm long. Finally, in order to recover the two TTAs from the SMB extract and raffinate streams, water was envisioned as a precipitation agent. Accordingly, the solubility of each TTA was measured in methanol/acetonitrile 70/30, 50/50, and 30/70 (%, v/v) modified with water. The obtained results showed that adding 65 % (%, v/v) of water it is possible to precipitate 98 % of the dissolved TTAs in all the tested methanol/acetonitrile mixtures.publishe

A class of Calogero type reductions of free motion on a simple Lie group

The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic values of the momentum map this leads to (new) spin Calogero type models. At some special values the `spin' degrees of freedom are absent and we obtain the standard $BC_n$ Sutherland model with three independent coupling constants from SU(n+1,n) and from SU(n,n). This generalization of the Olshanetsky-Perelomov derivation of the $BC_n$ model with two independent coupling constants from the geodesics on $G/G_+$ with G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character of $G_+$. The reductions considered permit further generalizations and work at the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and corrected some spelling error

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

Operator Mixing and the AdS/CFT correspondence

We provide a direct prescription for computing the mixing among gauge invariant operators in N=4 SYM. Our approach is based on the action of the superalgebra on the states of the theory and thus it can be also applied to resolve the mixing in the dual string description. As an example, we focus on the supermultiplet containing the BMN operators with two impurities. On the field theory side, we derive the leading planar quantum corrections to the naive expression of the highest weight state. Then we use the same prescription in the BMN limit of the AdS5xS5 string theory and derive the form of the 2-impurity highest weight state. The string expression matches nicely the SYM result and provides a prediction for the mixing due to higher order quantum corrections in field theory.Comment: 21 pages, 3 figures. Typos correcte