General relativistic treatment of LISA optical links

LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves in the band $10^{-5} - 1$ Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise etc. This is achieved by combining time-delayed data for which precise knowledge of time-delays is required. The gravitational field, mainly that of the Sun and the motion of LISA affect the time-delays and the optical links. Further, the effect of the gravitational field of the Earth on the orbits of spacecraft is included. This leads to additional flexing over and above that of the Sun. We have written a numerical code which computes the optical links, that is, the time-delays with great accuracy $\sim 10^{-2}$ metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with sufficient accuracy within $\sim 10$ metres for an integrated time window of about six days, when one of the arms tends to be tangent to the orbit. Our analysis of the optical links is fully general relativistic and the numerical code takes into account effects such as the Sagnac, Shapiro delay, etc.. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the configuration of LISA and in the physics, which may be used effectively to suppress the residual laser noise in the modified first generation TDI. We demonstrate our results for some important TDI variables

Optimising the directional sensitivity of LISA

It was shown in a previous work that the data combinations canceling laser frequency noise constitute a module - the module of syzygies. The cancellation of laser frequency noise is crucial for obtaining the requisite sensitivity for LISA. In this work we show how the sensitivity of LISA can be optimised for a monochromatic source - a compact binary - whose direction is known, by using appropriate data combinations in the module. A stationary source in the barycentric frame appears to move in the LISA frame and our strategy consists of "coherently tracking" the source by appropriately "switching" the data combinations so that they remain optimal at all times. Assuming that the polarisation of the source is not known, we average the signal over the polarisations. We find that the best statistic is the `network' statistic, in which case LISA can be construed of as two independent detectors. We compare our results with the Michelson combination, which has been used for obtaining the standard sensitivity curve for LISA, and with the observable obtained by optimally switching the three Michelson combinations. We find that for sources lying in the ecliptic plane the improvement in SNR increases from 34% at low frequencies to nearly 90% at around 20 mHz. Finally we present the signal-to-noise ratios for some known binaries in our galaxy. We also show that, if at low frequencies SNRs of both polarisations can be measured, the inclination angle of the plane of the orbit of the binary can be estimated.Comment: 16 pages, 8 figures, submitted to Phys Rev

Time Delay Interferometry for LISA with one arm dysfunctional

In order to attain the requisite sensitivity for LISA - a joint space mission of the ESA and NASA- the laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. By combining six appropriately time-delayed data streams containing fractional Doppler shifts - a technique called time delay interferometry (TDI) - the laser frequency noise may be adequately suppressed. We consider the general model of LISA where the armlengths vary with time, so that second generation TDI are relevant. However, we must envisage the possibility, that not all the optical links of LISA will be operating at all times, and therefore, we here consider the case of LISA operating with two arms only. As shown earlier in the literature, obtaining even approximate solutions of TDI to the general problem is very difficult. Since here only four optical links are relevant, the algebraic problem simplifies considerably. We are then able to exhibit a large number of solutions (from mathematical point of view an infinite number) and further present an algorithm to generate these solutions

Exact Tagged Particle Correlations in the Random Average Process

We study analytically the correlations between the positions of tagged particles in the random average process, an interacting particle system in one dimension. We show that in the steady state the mean squared auto-fluctuation of a tracer particle grows subdiffusively as $sigma^2(t) ~ t^{1/2}$ for large time t in the absence of external bias, but grows diffusively $sigma^2(t) ~ t$ in the presence of a nonzero bias. The prefactors of the subdiffusive and diffusive growths as well as the universal scaling function describing the crossover between them are computed exactly. We also compute $sigma_r^2(t)$, the mean squared fluctuation in the position difference of two tagged particles separated by a fixed tag shift r in the steady state and show that the external bias has a dramatic effect in the time dependence of $sigma_r^2(t)$. For fixed r, $sigma_r^2(t)$ increases monotonically with t in absence of bias but has a non-monotonic dependence on t in presence of bias. Similarities and differences with the simple exclusion process are also discussed.Comment: 10 pages, 2 figures, revte

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte

Drug utilization pattern and selected biochemical parameters in pre- and post-hemodialysis state in the end stage renal disease patients: a cross sectional study at a tertiary care hospital

Background: Chronic kidney disease can progress to end-stage kidney failure (ESRD), which is fatal without artificial filtering (dialysis) or a kidney transplant.Methods: The ESRD patients of either gender age >18 years who were diagnosed by nephrologist as ESRD and are on haemodialysis regularly included for the study.Results: The blood urea, serum creatinine, phosphorous, potassium levels were reduced significantly in post – haemodialysis condition, but, there was not much weight reduction after haemodialysis. Serum albumin, serum sodium and blood haemoglobin levels were almost unchanged in post – haemodialysis state. There was no significant difference between the pre and post haemodialysis parameters- serum Na+ serum albumin and blood hemoglobulin. Out of 75 ESRD patients, almost all patients 74 (98.7%) prescribed tablet Livogen, 73 (97.3%) patients given Inj. EPO, 55 (73.3%) tab Nicardia, 54 (76%) tab Sodamint, 43 (57.3%) capsule Alpha D3, 40 (53.3%) tab Shelcal. While between 12 (16%) to 20 (26%) patients prescribed tab Nodosis, tab Metoprolol, tab Febuget, tab Ecosprin, and tab Rantac. Only 1 (1.3%) to 9 (12%) patients received tablet Augmentin, tab Arkamine, tab Carvedilol, tab Para 500, tab Atorvas, Human mixtard, tab Calcicard, tab Minipress XL, tab Dytor, and tab Clopilet.Conclusions: The available two models of treatment, i.e., haemodialysis and poly pharmacy at hospital setup to face the challenges associated with the ESRD, and even outcome after application of both these two models of therapies did not provide optimal normal healthy life status to ESRD patients