Deformed Special Relativity and Deformed Symmetries in a Canonical Framework

In this paper we have studied the nature of kinematical and dynamical laws in $\kappa$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\kappa$-Minkowski phase space algebra that yields the $\kappa$-extended finite Lorentz transformations derived in \cite{kim}. This is a particular form of a Deformed Special Relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $\kappa$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and {\it{not}} $\kappa$-Minkowski) phase space algebra and Special Relativity Lorentz transformation (and {\it{not}} $\kappa$-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical $\kappa$-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the $\kappa$-particle.Comment: Revised version with change in Title and Abstract, No change in mathematical content, Reference section enlarged, Discussion on Soccer Ball Problem removed; Version to appear in PR

Development of a Fiber Optic Sensor for Online Monitoring of Thin Coatings

 The thickness measurement of gas, liquid and solid layers is not only important for the basic research on nanoscience but equally valuable in contemporary applied biomedical research. Here, we have developed an optical spectroscopy based technique for the online monitoring of thin films (coatings). A low cost light emitting diode (LED) source combined with a fiber optic bundle and grating based spectrograph have been used to generate white light interferogram. We have monitored online change of refractive index of an air film (~4 μm thickness) with temperature following the change in the intensity profile of the interferogram. A thin film of water between two cover slips (thin glass plates) has also been monitored. We have proposed a schematic for further lowering the cost of the developed instrument for the online monitoring of the coating thickness (semitransparent liquid/gas/solid films) during manufacturing/processing. A brief theoretical analysis on the detection limit of the developed technique has also been discussed in the paper

Understanding crop-ecology and agronomy of Rosa damascena Mill. for higher productivity

Abstract Crop-ecology and agronomic factors are the major determinants of crop growth and development. Medicinal and aromatic plants synthesize and store a variety of biochemical compounds. The secondary metabolites of Rosa damascena are used in the pharmaceutical, flavours, and fragrance industries. The rising demand of essential oil is causing an accelerated replacement of natural fragrance by synthetic fragrance. Out of 200 species of the genus Rosa, the R. damascena is the important essential oil bearing plant. The content and relative composition of major components of rose oil predominantly depend on temperature, light, soil, pruning, nutrient supply, harvesting time and other management factors. Natural rose oil is most expensive in the world market as compared to its synthetic substitute, and the global demand of high grade rose oil is likely to increase in near future. In order to meet the rising demand, reconciliation of crop-ecological and agronomical approaches is required. Thus, there is pressing need to understand how these two factors and their interaction would provide noble strategies to stabilize yield of R. damascena in fluctuating environment. We do not attempt comprehensive review on R. damascena, rather we focus on crop ecology and agronomy, which determine the yield of flower and secondary metabolites

Lie Particle And Its Batalin-Tyutin Extension

In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature, in particular isomorphic to the angular momentum algebra. The work is in the spirit of our earlier works in this connection, {\it {i.e.}} PLB 618 (2005)243 and PLB 623 (2005)251, where the $\kappa$-Minkowski form of noncomutative spacetime was considered. This non-linear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantization. This prompts us to embed the model in the Batalin-Tyutin extended space where the equivalent model comprises of phase space variables satisfying a canonical algebra. We also compare our present model with the point particle model, previously proposed by us, in the context of $\kappa$-Minkowski spacetime.Comment: Latex, 10 pages, enlarged and modified version, no changes in results and conslusions, one reference added, to appear in Phys.Lett.

Constrained Dynamics of an Anomalous (g/neq2)(g/neq 2) Relativistic Spinning Particle in Electromagnetic Background

In this paper we have considered the dynamics of an anomalous ($g\neq 2$) charged relativistic spinning particle in the presence of an external electromagnetic field. The constraint analysis is done and the complete set of Dirac brackets are provided that generate the canonical Lorentz algebra and dynamics through Hamiltonian equations of motion. The spin-induced effective curvature of spacetime and its possible connection with Analogue Gravity models are commented upon.Comment: 10 pages Latex, minor corrections and changes in ref., slightly enlarged version, to appear in EPJ

Understanding crop-ecology and agronomy of Rosa damascena Mill. for higher productivity

Crop-ecology and agronomic factors are the major determinants of crop growth and development. Medicinal and aromatic plants synthesize and store a variety of biochemical compounds. The secondary metabolites of Rosa damascena are used in the pharmaceutical, flavours, and fragrance industries. The rising demand of essential oil is causing an accelerated replacement of natural fragrance by synthetic fragrance. Out of 200 species of the genus Rosa, the R. damascena is the important essential oil bearing plant. The content and relative composition of major components of rose oil predominantly depend on temperature, light, soil, pruning, nutrient supply, harvesting time and other management factors. Natural rose oil is most expensive in the world market as compared to its synthetic substitute, and the global demand of high grade rose oil is likely to increase in near future. In order to meet the rising demand, reconciliation of crop-ecological and agronomical approaches is required. Thus, there is pressing need to understand how these two factors and their interaction would provide noble strategies to stabilize yield of R. damascena in fluctuating environment. We do not attempt comprehensive review on R. damascena, rather we focus on crop ecology and agronomy, which determine the yield of flower and secondary metabolites

Non-destructive estimation of chlorophyll and nitrogen content in leaf of Rosa damascena (Mill)

Chlorophyll (Chl) and nitrogen (N) status of leaves provide valuable information about the physiological condition of plants. The conventional methods for measuring Chl and N contents in leaves are destructive, costly, time-consuming, and do not allow repetitive measurement of the same sample. The Damask Rose (Rosa damascena Mill) is an important aromatic crop in the western Himalaya region in India. Generally, flower yield and oil yield of the Damask rose are correlated with nitrogen, phosphorus, and potassium (NPK) levels in the leaf at the bud development stage. The dynamics of N within the rose plant have not been reported clearly. Thus, there is a pressing need for non-destructive techniques to estimate Chl and N content in the leaf of the Damask rose. Our objective was to establish an appropriate mathematical relationship between the Chl content index (CCI) value and the total Chl/N contents for non-destructive estimation of total Chl and N in the leaf of the Damask rose. The regression models were developed with destructively measured parameters (total Chl and N) as the dependent variable and a parameter derived from CCM-200 as the independent variable (CCI). We found that polynomial regression models are suitable for non-destructive estimation of total Chl, and the model predicted values were very close to traditionally measured values with a root mean square prediction error (RMSEp) less than 0.20 mgg ˉ1 of Chl. In the case of N estimation, a power regression model was appropriate with lowest Akaike’s information criteria (AIC) and root mean square validated error (RMSEv) value. Significant correlations (P≤0.001) were observed between traditionally measured values and our model predicted values in both cases