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In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.

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We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, Ω_{cr}, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the Ω_{cr} values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional s-wave scattering lengths through the strength of nonlinear rotation, C, such that Ω_{cr}(C>0)<Ω_{cr}(C=0)<Ω_{cr}(C<0). In an analogous manner, the critical ellipticity (ε_{cr}) for vortex nucleation during an adiabatic introduction of trap ellipticity (ε) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.

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Breast cancer is the most prevalent cancer in women around the world, having a sudden spread nowadays because of the poor sedentary lifestyle of people. Comprising several subtypes, one of the most dangerous and aggressive ones is triple-negative breast cancer or TNBC. Even though conventional surgical approaches like single and double mastectomy and preventive chemotherapeutic approaches are available, they are not selective to cancer cells and are only for symptomatic treatment. A new branch called nanotechnology has emerged in the last few decades that offers various novel characteristics, such as size in nanometric scale, enhanced adherence to multiple targeting moieties, active and passive targeting, controlled release, and site-specific targeting. Among various nanotherapeutic approaches like dendrimers, lipid-structured nanocarriers, carbon nanotubes, etc., nanoparticle targeted therapeutics can be termed the best among all for their specific cytotoxicity to cancer cells and increased bioavailability to a target site. This review focuses on the types and molecular pathways involving TNBC, existing treatment strategies, various nanotechnological approaches like exosomes, carbon nanotubes, dendrimers, lipid, and carbon-based nanocarriers, and especially various nanoparticles (NPs) like polymeric, photodynamic, peptide conjugated, antibody-conjugated, metallic, inorganic, natural product capped, and CRISPR based nanoparticles already approved for treatment or are under clinical and pre-clinical trials for TNBC.

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By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskii equation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a single traveling solitary wave. The sign of the current nonlinearity determines the direction of propagation of the emerging solitons.

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BACKGROUND: AdipoRon is the first synthetic analog of endogenous adiponectin, an adipose tissue-derived hormone. AdipoRon possesses pharmacological properties similar to adiponectin and its ability to bind and activate the adipoR1 and adipoR2 receptors makes it a suitable candidate for the treatment of a multitude of disorders. OBJECTIVE: In the present review, an attempt was made to compile and discuss the efficacy of adipoRon against various disorders. RESULTS: AdipoRon is a drug that acts not only in metabolic diseases but in other conditions unrelated to energy metabolism. It is well- reported that adipoRon exhibits strong anti-obesity, anti-diabetic, anticancer, anti-depressant, anti-ischemic, anti-hypertrophic properties and also improves conditions like post-traumatic stress disorder, anxiety, and systemic sclerosis. CONCLUSION: A lot is known about its effects in experimental systems, but the translation of this knowledge to the clinic requires studies which, for many of the potential target conditions, have yet to be carried out. The beneficial effects of AdipoRon in novel clinical conditions will suggest an underlying pathophysiological role of adiponectin and its receptors in previously unsuspected settings.

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