Abstract:We study rigidly rotating strings in κ-deformed AdS background. We probe this classically integrable background with 'spiky' strings and analyze the string profiles in the large charge limit systematically. We also discuss the dispersion relation among the conserved charges for these solutions in long string limit.

Magnetic nanoparticles as drug carriers, despite showing immense promises in preclinical trials, have remained to be only of limited use in real therapeutic practice primarily due to unresolved anomalies concerning their grossly contrasting controllability and variability in performance in artificial test benches as compared to human tissues. To circumvent the deficits of reported in vitro drug testing platforms that deviate significantly from the physiological features of the living systems and result in this puzzling contrast, here, we fabricate a biomimetic microvasculature in a flexible tissue phantom and demonstrate distinctive mechanisms of magnetic-field-assisted controllable penetration of biocompatible iron oxide nanoparticles across the same, exclusively modulated by tissue deformability, which has by far remained unraveled. Our experiments deciphering the transport of magnetic nanoparticles in a blood analogue medium unveil a decisive interplay of the flexibility of the microvascular pathways, magnetic pull, and viscous friction toward orchestrating the optimal vascular penetration and targeting efficacy of the nanoparticles in colorectal tissue-mimicking bioengineered media. Subsequent studies with biological cells confirm the viability of using localized magnetic forces for aiding nanoparticle penetration within cancerous lesions. We establish nontrivially favorable conditions to induce a threshold force for vascular rupture and eventual target of the nanoparticles toward the desired extracellular site. These findings appear to be critical in converging the success of in vitro trials toward patient-specific targeted therapies depending on personalized vascular properties obtained from medical imaging data.

Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal perturbations of the spiky string worldsheets embedded in a 2+1 dimensional flat spacetime. Such perturbations lead to a rounding off of the spikes, which, in a way, demonstrates the stable nature of the unperturbed worldsheet. The same features appear for the dual spiky string solution and in the spiky as well as their dual solutions in 3 + 1 dimensional flat spacetime. Our results are based on exact solutions of the corresponding Jacobi equations which we obtain and use while constructing the profiles of the perturbed configurations.

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Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS 3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.