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We explore the self-propulsion of an active Ornstein-Uhlenbeck particle with a non-linear velocity dependent friction. Using analytical approach and numerical simulation, we have exactly investigated the dynamical behaviour of the particle in terms of particle trajectory, position and velocity distribution functions in both underdamped as well as overdamped regimes of the dynamics. Analyzing the distribution functions, we observe that for a confined harmonic particle, with an increase in duration of self-propulsion, the inertial particle prefers to accumulate near the boundary of the confinement rather than the mean position, reflecting an activity induced bistability in the presence of nonlinear friction. On the other hand, in the overdamped or highly viscous regime, where the inertial influence is negligible small, the sharp peak structure in the distribution across the mean position of the well reveals as usual trapping of the particle with increase in the persistent duration of activity. Moreover, for a free particle, using perturbation method, we have analytically computed the velocity distribution function in the vanishing limit of noise. The distribution interestingly shows the similar attributes as in case of a harmonic well, thus providing an additional effective confining mechanism that can be explained as a decreasing function of effective temperature. In this limit, the analytically computed distribution agrees well with the simulation results., Comment: 9 pages, 6 figures

Magnetic topological insulators (TIs) herald a wealth of applications in spin-based technologies, relying on the novel quantum phenomena provided by their topological properties. Particularly promising is the (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ layered family of established intrinsic magnetic TIs that can flexibly realize various magnetic orders and topological states. High tunability of this material platform is enabled by manganese-pnictogen intermixing, whose amounts and distribution patterns are controlled by synthetic conditions. Positive implication of the strong intermixing in MnSb$_2$Te$_4$ is the interlayer exchange coupling switching from antiferromagnetic to ferromagnetic, and the increasing magnetic critical temperature. On the other side, intermixing also implies atomic disorder which may be detrimental for applications. Here, we employ nuclear magnetic resonance and muon spin spectroscopy, sensitive local probe techniques, to scrutinize the impact of the intermixing on the magnetic properties of (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ and MnSb$_2$Te$_4$. Our measurements not only confirm the opposite alignment between the Mn magnetic moments on native sites and antisites in the ground state of MnSb$_2$Te$_4$, but for the first time directly show the same alignment in (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ with n = 0, 1 and 2. Moreover, for all compounds, we find the static magnetic moment of the Mn antisite sublattice to disappear well below the intrinsic magnetic transition temperature, leaving a homogeneous magnetic structure undisturbed by the intermixing. Our findings provide a microscopic understanding of the crucial role played by Mn-Bi intermixing in (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ and offer pathways to optimizing the magnetic gap in its surface states., Comment: 13 pages, 4 figures (Main) and 8 pages, 10 figures (Supplemental)

We investigate the self-propulsion of an inertial active particle confined in a two-dimensional harmonic trap. The particle is suspended in a non-Newtonian or viscoelastic suspension with a friction kernel that decays exponentially with a time constant characterizing the memory timescale or transient elasticity of the medium. By solving the associated non-Markovian dynamics, we identify two regimes in parameter space distinguishing the oscillatory and non-oscillatory behavior of the particle motion. By simulating the particle trajectories and exactly calculating the steady state probability distribution functions and mean square displacement, interestingly, we observe that with an increase in the memory time scale, the elastic bound of suspension dominates over the influence of harmonic trap. As a consequence, the particle can escape out of the trap without approaching steady state. On the other hand, with an increase in the duration of the activity, the particle becomes trapped by the harmonic confinement., Comment: 9 pages, 6 figures

We consider the dynamics of a charged inertial active Ornstein-Uhlenbeck particle in a viscoelastic suspension under the action of an uniform magnetic field. With the help of both numerical simulation and analytical framework, we exactly investigate the viscoelastic response of the particle to the magnetic field by means of particle trajectories, mean displacement, and mean square displacement (MSD) calculations. The simulated particle trajectories and MSD calculations reveal that the steady state response of a confined harmonic particle to the magnetic field show interesting features due to the complex interplay of underlying physical processes such as elastic dissipation and active fluctuations in the medium. When the activity time scale of the dynamics is larger than the elastic dissipation timescale (or vice-versa), the steady state MSD shows an enhancement (or suppression) with increase in the field strength. In both the cases, for very strong magnetic field the MSD interestingly approaches the value at the equilibrium limit where the generalized fluctuation dissipation relation is satisfied and the particle behaves like an inertial passive Brownian particle. Thus, for a finite magnetic field, the system exhibits a re-entrant type transition from active to passive and then to active behaviour with persistence of elastic dissipation in the medium. However, for a free particle, the overall displacement covered always gets suppressed with increase in the strength of the magnetic field and finally approaches zero for a very strong magnetic field., Comment: 10 pages, 5 figures

We consider an inertial active Ornstein-Uhlenbeck particle self-propelling in a saw-tooth ratchet potential. Using the Langevin simulation and matrix continued fraction method, the particle transport, steady state diffusion, and coherence in transport are investigated throughout the ratchet. Spatial asymmetry is found to be the key criterion for the possibility of directed transport in the ratchet. Interestingly, the simulated particle trajectories and the corresponding position and velocity distribution functions reveal that the system passes through an activity-induced transition in the transport from the running phase to the locked phase with the self-propulsion/activity time of the dynamics. This is further corroborated by the mean square displacement (MSD) calculation. The MSD gets suppressed with increase in the persistence of activity in the medium and finally approaches zero for very large value of self propulsion time, reflecting a kind of trapping of the particle by the ratchet for longer persistent of activity in the medium. The non-monotonic behaviour of the particle current and Peclet number with self propulsion time confirms that the particle transport and it's coherence can be enhanced or reduced by fine tuning the persistent duration of activity. Moreover, for an intermediate range of self-propulsion time in the dynamics as well as for an intermediate range of mass of the particle, even though the particle current shows a pronounced unusual maximum with mass, there is no enhancement in the Peclet number, instead the Peclet number decreases with mass, confirming the degradation of coherence in transport. Finally, from the analytical calculations, it is observed that for a highly viscous medium, where the inertial influence is negligibly small, the particle current approaches the current in the over damped regime., Comment: 7 figures

We study the dynamics of an inertial active Ornstein-Uhnlenbeck particle self-propelling in a confined harmonic well. The transport behaviour of the particle is investigated by analyzing the particle trajectories, steady state correlations, and mean square displacement (MSD). The steady state correlation functions for the position as well as velocity are exactly calculated using different methods. We explore how the inertia affects the dynamical behaviour, when the particle is confined in a harmonic trap as well as when it is set free. From the exact calculation of MSD, it is observed that the initial time regimes are ballistic for both harmonically confined particle and free particle, whereas the long time regimes are diffusive for a free particle and non diffusive for a harmonically confined particle. One of our interesting observation is that the harmonically confined particle gets more and more confined with increase in the self propulsion time or activity time of the dynamics and finally it gets trapped for very large self propulsion time. For a free particle, the velocity correlation decays by the complex interplay between the inertial time scale and the self propulsion time scale of the dynamics. Moreover, decorrelation in velocity happens only when these two time scales are of equal order., Comment: 9 pages, 7 figures

We consider an inertial active Ornstein-Uhlenbeck particle in an athermal bath. The particle is charged, constrained to move in a two-dimensional harmonic trap, and a magnetic field is applied perpendicular to the plane of motion. The steady state correlations and the mean square displacement are studied when the particle is confined as well as when it is set free from the trap. With the help of both numerical simulation and analytical calculations, we observe that inertia plays a crucial role in the dynamics in the presence of a magnetic field. In a highly viscous medium where the inertial effects are negligible, the magnetic field has no influence on the correlated behaviour of position as well as velocity. In the time asymptotic limit, the overall displacement of the confined harmonic particle gets enhanced by the presence of magnetic field and saturates for a stronger magnetic field. On the other hand, when the particle is set free, the overall displacement gets suppressed and approaches zero when strength of the field is very high. Interestingly, it is seen that in the time asymptotic limit, the confined harmonic particle behaves like a passive particle and becomes independent of the activity, especially in the presence of a very strong magnetic field. Similarly, for a free particle the mean square displacement in the long time limit becomes independent of activity even for a longer persistence of noise correlation in the dynamics., Comment: Phys. Rev. E (Accepted), 9 pages, 6 figures

Being a dual purpose enzyme, the DNA polymerase is responsible for elongation of the newly formed DNA strand as well as cleaving the erroneous growth in case of a misincorporation. The efficiency of replication depends on the coordination of the polymerization and exonuclease activity of DNA polymerase. Here we propose and analyze a minimal kinetic model of DNA replication and determine exact expressions for the velocity of elongation and the accuracy of replication. We first analyze the case without exonuclease activity. In that case, accuracy is determined by a kinetic competition between stepping and unbinding, with discrimination between correct and incorrect nucleotides in both transitions. We then include exonuclease activity and ask how different modes of additional discrimination in the exonuclease pathway can improve the accuracy while limiting the detrimental effect of exonuclase on the speed of replication. In this way, we ask how the kinetic parameters of the model have to be set to coordinate the two activities of the enzyme for high accuracy and high speed. The analysis also shows that the design of a replication system does not universally have to follow the speed-accuracy trade-off rule, although it does in the biologically realized parameter range. The accuracy of the process is mainly controlled by the crucial role of stepping after erroneous incorporation, which has impact on both polymerase and exonuclease activities of DNA polymerase.

We consider a dilute suspension of active (self-propelling) particles in a visco-elastic fluid. Particles are charged and constrained to move in a two dimensional harmonic trap. Their dynamics is coupled to a constant magnetic field applied perpendicular to their motion via Lorentz force. Due to the finite activity, the generalised fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation time scale of the medium is larger (smaller) than the persistence time scale of the self-propelling particles, the system is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a novel transition from diamagnetic to paramagnetic state (and vice-versa) simply by tuning the time scales of underlying physical processes, such as, active fluctuations and visco-elastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves non-monotonically with respect to increasing persistence of self-propulsion, that drives the system out of equilibrium, Comment: 9 pages

The paper considers the system of pressureless gas dynamics in one space dimension. The question of solvability of the initial-boundary value problem is addressed. Using the method of generalized potentials and characteristic triangles, extended to the boundary value case, an explicit way of constructing measure-valued solutions is presented. The prescription of boundary data is shown to depend on the behavior of the generalized potentials at the boundary. We show that the constructed solution satisfies an entropy condition and it conserves mass, whereby mass may accumulate at the boundary. Conservation of momentum again depends on the behavior of the generalized boundary potentials. There is a large amount of literature where the initial value problem for the pressureless gas dynamics model has been studied. To our knowledge, this paper is the first one which considers the initial-boundary value problem.

We present the structural and magnetic properties of KNaCuP$_2$O$_7$ investigated via x-ray diffraction, magnetization, specific heat, and $^{31}$P NMR and $^{23}$Na NMR measurements and complementary electronic structure calculations. The temperature dependent magnetic susceptibility and $^{31}$P NMR shift could be modeled very well by the uniform spin-$1/2$ Heisenberg antiferromagnetic chain model with nearest-neighbour interaction $J/k_{\rm B}\simeq 58.7$ K. The corresponding mapping using first principles electronic structure calculations leads to $J^{\rm DFT}/k_{\rm B} \simeq 59$ K with negligibly small inter-chain couplings ($J^{\prime}/k_{\rm B}$, $J^{\prime \prime}/k_{\rm B} < 0.1$ K), further confirming that the system is indeed an one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet. The temperature-dependent unit cell volume could be described well using the Debye approximation with a Debye temperature of $\Theta_{\rm D} \simeq 294$ K, consistent with the heat capacity data. The diverging trend of the NMR spin-lattice relaxation rates ($^{31}1/T_1$ and $^{23}1/T_1$) imply the onset of a magnetic long-range-ordering at very low temperatures supporting the anticipated $T_{\rm N} \simeq 0.38$ K from the inter-chain couplings. Moreover, the NMR spin-lattice relaxation rates show the dominant contributions from uniform ($q=0$) and staggered ($q = \pm \pi/a$) spin fluctuations in the high and low temperature regimes, respectively mimicking one-dimensionality of the spin-lattice. We have also demonstrated that $^{31}1/T_1$ in high temperatures varies linearly with $1/\sqrt{H}$ reflecting the effect of spin diffusion on the dynamic susceptibility. Further, the inter-chain frustration also substantially impede the magnetic ordering rendering the spin-lattice a perfect one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet over a wide temperature range., Comment: 15 pages, 13 figures, 1 table

X-ray diffraction, thermodynamic measurements, and density-functional band-structure calculations are used to study the magnetic behavior of BaCuTe$_{2}$O$_{6}$, a member of the $A$CuTe$_2$O$_6$ structural family that hosts complex three-dimensional frustrated spin networks with possible spin-liquid physics. Temperature-dependent magnetic susceptibility and heat capacity of the Ba compound are well described by the one-dimensional spin-$\frac12$ Heisenberg chain model reminiscent of the Sr analog SrCuTe$_2$O$_6$. While the intrachain coupling $J/k_{\rm B}\simeq 37$ K is reduced compared to 49 K in the Sr compound, the N\'eel temperature increases from 5.5 K (Sr) to 6.1 K (Ba). Unlike the Sr compound, BaCuTe$_2$O$_6$ undergoes only one magnetic transition as a function of temperature and shows signatures of weak spin canting. We elucidate the microscopic difference between the Sr and Ba compounds and suggest that one of the interchain couplings changes sign as a result of negative pressure caused by the Sr/Ba substitution. The N\'eel temperature of BaCuTe$_2$O$_6$ is remarkably insensitive to the magnetic dilution with Zn$^{2+}$ up to the highest reachable level of about 20%., Comment: 10 pages, 11 figures, 3 tables, Accepted in Phys. Rev. B

We present the synthesis and a detail investigation of structural and magnetic properties of polycrystalline [VO(HCOO)$_2\cdot$(H$_2$O)] by means of x-ray diffraction, magnetic susceptibility, high-field magnetization, heat capacity, and electron spin resonance measurements. It crystallizes in a orthorhombic structure with space group $Pcca$. It features distorted VO$_6$ octahedra connected via HCOO linker (formate anions) forming a two-dimensional square lattice network with a bilayered structure. Analysis of magnetic susceptibility, high field magnetization, and heat capacity data in terms of the frustrated square lattice model unambiguously establish quasi-two-dimensional nature of the compound with nearest neighbour interaction $J_1/k_{\rm B} \simeq 11.7$~K and next-nearest-neighbour interaction $J_2/k_{\rm B} \simeq 0.02$~K. It undergoes a N\'eel antiferromagnetic ordering at $T_{\rm N} \simeq 1.1$~K. The ratio $\theta_{\rm CW}/T_{\rm N} \simeq 10.9$ reflects excellent two-dimensionality of the spin-lattice in the compound. A strong in-plane anisotropy is inferred from the linear increase of $T_{\rm N}$ with magnetic field, consistent with the structural data., Comment: 9 pages, 7 figures, 1 table

Prediction of low-mass $W_R$ and $Z_R$ gauge bosons in popular grand unified theories has been the subject of considerable attention over the last three decades. In this work we show that when gravity induced corrections due to dim.5 operator are included the minimal symmetry breaking chain of $SO(10)$ and $E_6$ GUTs can yield $W_R^{\pm}$ and $Z_R$ bosons with masses in the range $(3-10)$ TeV which are accessible to experimental tests at the Large Hordan Collider. The RH neutrinos turn out to be heavy pseudo-Dirac fermions. The model can fit all fermion masses and manifest in rich structure of lepton flavor violation while proton life time is predicted to be much longer than the accessible limit of Super-Kamiokande or planned Hyper-Kamiokande collaborations., Comment: 3 pages LaTeX, Submitted to ICHEP-2014, Valencia, Spain; To appear in Nuclear and Particle Physics Proceedings

In the present paper, the notion of Lidstone Fractal Interpolation Function ($Lidstone \ FIF$) is introduced to interpolate and approximate data generating functions that arise from real life objects and outcomes of several scientific experiments. A Lidstone FIF extends the classical Lidstone Interpolation Function which is generally found not to be satisfactory in interpolation and approximation of such functions. For a data $\{(x_n,y_{n,2k}); n=0,1,\ldots,N \ \text{and} \ k=0,1,\ldots,p\}$ with $N,p\in\mathbb{N}$, the existence of Lidstone FIF is proved in the present work and a computational method for its construction is developed. The constructed Lidstone FIF is a $C^{2p}[x_0,x_N]$ fractal function $\ell_\alpha$ satisfying $\ell_\alpha^{(2k)}(x_n)=y_{n,2k}$, $n=0,1,\ldots,N$,\ $k=0,1,\ldots,p$. Our error estimates establish that the order of $L^\infty$-error in approximation of a data generating function in $C^{2p}[x_0,x_N]$ by Lidstone FIF is of the order $N^{-2p}$, while $L^\infty$-error in approximation of $2k$-order derivative of the data generating function by corresponding order derivative of Lidstone FIF is of the order $N^{-(2p-2k)}$. The results found in the present work are illustrated for computational constructions of a Lidstone FIF and its derivatives with an example of a data generating function., Comment: 20 pages, 3 figures