Multidimensional persistence behaviour in an Ising system

We consider a periodic Ising chain with nearest-neighbour and $r$-th neighbour interaction and quench it from infinite temperature to zero temperature. The persistence probability $P(t)$, measured as the probability that a spin remains unflipped upto time $t$, is studied by computer simulation for suitable values of $r$. We observe that as time progresses, $P(t)$ first decays as $t^{-0.22}$ (-the {\em first} regime), then the $P(t)-t$ curve has a small slope (in log-log scale) for some time (-the {\em second} regime) and at last it decays nearly as $t^{-3/8}$ (-the {\em third} regime). We argue that in the first regime, the persistence behaviour is the usual one for a two-dimensional system, in the second regime it is like that of a non-interacting (`zero-dimensional') system and in the third regime the persistence behaviour is like that of a one dimensional Ising model. We also provide explanations for such behaviour.Comment: 6 pages, 12 figure

A Small World Network of Prime Numbers

According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers : $n = p + q$. We construct a network where each node is a prime number and corresponding to every even number $n$, we put a link between the component primes $p$ and $q$. In most cases, an even number can be broken up in many ways, and then we chose {\em one} decomposition with a probability $|p - q|^{\alpha}$. Through computation of average shortest distance and clustering coefficient, we conclude that for $\alpha > -1.8$ the network is of small world type and for $\alpha < -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.Comment: 6 pages, 10 figure

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa=0.5$ and $\Gamma=0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa=0.5$, $\Gamma=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.Comment: 11 pages, 11 figure

Dual role of nanoparticles as drug carrier and drug.

The conventional chemotherapeutic agents used in the treatment of human malignancies are directed nonspecifically against both malignant and nonmalignant cells, often limiting their efficacy with having serious side effects. Recent development of drug delivery vehicles has opened up the possibility of targeted drug delivery systems with the potential of achieving maximum efficacy with minimal toxicity. The possibility of using a nanomaterial as a combinational drug component is intuitively evident as it would compensate the toxicity level by enhancing drug delivery efficiency. Additionally, cell-specific cytotoxicity (reported earlier by our group) of the nanovehicle itself may potentiate a more effective targeted cell killing. In this paper, we explore the possibility of using gold nanoparticles playing the dual role of an anticancer agent and a carrier of a chemotherapeutic drug. This is demonstrated using vincristine sulfate (VS), salt of an alkaloid often used in the treatment of multiple myeloma (MM), and U266 as a test MM cell line. The drug VS shows the expected G2-M-phase arrest of cells. Notably, bare gold nanoparticle shows arrest of the S phase cells that may be particularly important in case of slow-growing malignancies like MM where most of the cells remain in G1 phase of the cell cycle. The VS conjugated gold retains the activity of both gold nanoparticle and VS leading to a synergistic rise of the apoptotic cell population

Comparison of transvaginal sacrospinous ligament fixation with abdominal sacrocolpopexy in treatment of post-hysterectomy vault prolapse-a prospective randomized study

Background: Vaginal vault prolapse is a common condition following abdominal or vaginal hysterectomy causing negative impact on women’s quality of life. The study compares the efficacy of abdominal and vaginal route surgery in correcting post-hysterectomy vault prolapse by postoperative assessment and at least twelve months follow up.Methods: A prospective comparative study among post-hysterectomy patients attending the GOPD of Midnapore Medical College diagnosed as vaginal vault prolapse at least stage2 between January 2013 to December 2019. The study population included 31 women divided into two groups-group A included 16 women underwent unilateral sacrospinous ligament fixation (SSF) and group B included 15 women underwent abdominal sacrocolpopexy (ASC).Results: There was no significant difference between the two groups in terms of mean age, mean weight, mean parity and BMI, hence both groups are comparable. The mean operating time was 117±19.68 min in ASC group and 83.25±11.28 min in SSF group (p<0.005); significant mean blood loss was reported in ASC group (373±97.79 ml in ASC group versus 193.125±98.97 ml in SSF group, p<0.005), more hospital stays in ASC group (p<0.005) and more post operative complications in ASC group than SSF group. At follow up, the mean vaginal length showed significantly longer for ASC group than that of SSF group (p<0.005).Conclusions: ASC and SSF, both techniques are effective in management of vault prolapse in hands of an expert though recovery time is much quicker in SSF group.

Spin-spin Correlation in Some Excited States of Transverse Ising Model

We consider the transverse Ising model in one dimension with nearest-neighbour interaction and calculate exactly the longitudinal spin-spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use Fisher-Hartwig conjecture. The result is that the correlation decays algebraically with distance ($n$) as $1/\surd n$ and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.Comment: 5 pages, 1 figur

Floating Phase in 2D ANNNI Model

We investigate whether the floating phase (where the correlation length is infinite and the spin-spin correlation decays algebraically with distance) exists in the temperature($T$) - frustration parameter ($\kappa$) phase diagram of 2D ANNNI model. To identify this phase, we look for the region where (i) finite size effect is prominent and (ii) some relevant physical quantity changes somewhat sharply and this change becomes sharper as the system size increases. For $\kappa < 0.5$, the low temperature phase is ferromagnetic and we study energy and magnetization. For $\kappa > 0.5$, the low temperature phase is antiphase and we study energy, layer magnetization, length of domain walls running along the direction of frustration, number of domain-intercepts that are of length 2 along the direction of frustration, and the number of domain walls that do not touch the upper and/or lower boundary. In agreement with some previous studies, our final conclusion is that, the floating phase exists, if at all, only along a line.Comment: 9 pages, 17 figure

Whole-Genome Sequence of Drug-Resistant Mycobacterium tuberculosis Strain S7, Isolated from a Patient with Pulmonary Tuberculosis

Over the past decades, drug-resistant Mycobacterium tuberculosis strains have presented a significant challenge, with inadequate diagnosis of tuberculosis (TB) cases. Here, we report the draft whole-genome sequence of drug-resistant M. tuberculosis strain S7, which was isolated from a patient from Tripura, India, who was diagnosed with pulmonary TB