Simple Analytical Formula Research Articles

Positive-Negative Birefringence in Multiferroic Layered Metasurfaces.

We uncover and identify the regime for a magnetically and ferroelectrically controllable negative refraction of a light-traversing multiferroic, oxide-based metastructure consisting of alternating nanoscopic ferroelectric (SrTiO3) and ferromagnetic (Y3Fe2(FeO4)3, YIG) layers. We perform analytical and numerical simulations based on discretized, coupled equations for the self-consistent Maxwell/ferroelectric/ferromagnetic dynamics and obtain a biquadratic relation for the refractive index. Various scenarios of ordinary and negative refraction in different frequency ranges are analyzed and quantified by simple analytical formula that are confirmed by full-fledge numerical simulations. Electromagnetic waves injected at the edges of the sample are propagated exactly numerically. We discovered that, for particular GHz frequencies, waves with different polarizations are characterized by different signs of the refractive index, giving rise to novel types of phenomena such as a positive-negative birefringence effect and magnetically controlled light trapping and accelerations.

An analytic hydrodynamical model of rotating 3D expansion in heavy-ion collisions

A new exact and analytic solution of non-relativistic fireball hydrodynamics is presented. It describes an expanding three-axis ellipsoid that rotates along one of its principal axes. The observables are calculated using simple analytic formulas. Following earlier works, it is pointed out that azimuthal oscillation of the off-diagonal Bertsch-Pratt radii of Bose-Einstein correlations as well as rapidity dependent directed and third flow measurements provide means to determine the magnitude of the rotation of the fireball. It is argued that observing this rotation and its dependence on collision energy may lead to new information on the equation of state of the strongly interacting quark gluon plasma produced in high energy heavy ion collisions.

Bending stiff charged polymers: The electrostatic persistence length

Many charged polymers, including nucleic acids, are locally stiff. Their bending rigidity —quantified by the persistence length— depends crucially on Coulombic features, such as the ionic strength of the solution which offers a convenient experimental route for tuning the rigidity. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. Specified to double-stranded DNA, our work reveals that the widely used bare persistence length of 500 Å is overestimated by some 20%.

Evolution of an electromagnetic field in the presence of a mobile membrane

We consider a one-dimensional cavity composed of two perfect, fixed mirrors and a mobile membrane in between. Assuming that the membrane starts to move from rest and that the membrane moves appreciably in a time-scale much larger than the time-scale in which the cavity electromagnetic field evolves appreciably, we derive simple analytic formulas that describe to good approximation the evolution of the field and that provide an intuitive physical picture. These formulas take into account the position, velocity, and acceleration of the membrane and are valid for arbitrarily large displacements of the membrane along the cavity axis. Also, we deduce the conditions under which the field can be described to good approximation by a single instantaneous mode.

Towards TDDFT for Strongly Correlated Materials

We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch–Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO3. We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO3, a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.

Light helicity detection in MOS-based spin-photodiodes: An analytical model

In a metal-oxide-semiconductor-based spin-photodiode, the helicity of an incoming light is efficiently converted into an electrical signal by exploiting (i) the helicity dependence of the degree of optical spin orientation for photogenerated carriers in the semiconductor and (ii) the spin-dependent tunneling transmission of the insulating barrier between the semiconductor and a ferromagnetic metal. Here, we propose a theoretical model for predicting the electrical response of the device to a circularly polarized light, by integrating the Fert-Jaffrès framework [A. Fert and H. Jaffrès, Phys. Rev. B 64, 184420 (2001)] with a helicity-dependent photo-generation term. A figure of merit, related to the variation of the electrical response to the switching of the light helicity from right to left, is defined, and its dependence on the constitutive parameters of the device (barrier resistivity and spin selectivity, semiconductor resistivity and spin diffusion length) is shown. Finally, a simple analytical formula for identifying the optimal resistance barrier leading to the maximum efficiency is found and experimentally validated on Fe/MgO/Ge spin-photodiodes.

Optimization of the Tilted-Pulse-Front Terahertz Excitation Setup Containing Telescope

Optimization of the telescopic tilted-pulse-front terahertz excitation setup with respect to the imaging errors is given. A guideline is presented in the form of simple analytical formulae describing the optimal geometrical configuration of the telescopic setup. Pump pulse distortions and terahertz wave-front distortions are analyzed by ray tracing calculations supposing near-infrared pump pulses with 200 fs transform limited pulse length. The detrimental effects of imaging errors in a tilted-pulse-front terahertz source can be significantly reduced by using telescopic imaging instead of one-lens. It is also shown, that in the case of the one-lens setup significant, and in the case of the telescopic setup, less significant reduction of the imaging errors can be achieved by using achromat lens(es) instead of singlet one(s). Calculation results show that the telescopic setup consisting of two achromat lenses is the most promising choice among the practically relevant schemes.

Depletion region surface effects in electron beam induced current measurements.

Electron beam induced current (EBIC) is a powerful characterization technique which offers the high spatial resolution needed to study polycrystalline solar cells. Current models of EBIC assume that excitations in the p-n junction depletion region result in perfect charge collection efficiency. However we find that in CdTe and Si samples prepared by focused ion beam (FIB) milling, there is a reduced and nonuniform EBIC lineshape for excitations in the depletion region. Motivated by this, we present a model of the EBIC response for excitations in the depletion region which includes the effects of surface recombination from both charge-neutral and charged surfaces. For neutral surfaces we present a simple analytical formula which describes the numerical data well, while the charged surface response depends qualitatively on the location of the surface Fermi level relative to the bulk Fermi level. We find the experimental data on FIB-prepared Si solar cells is most consistent with a charged surface, and discuss the implications for EBIC experiments on polycrystalline materials.

Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method

Low-order thermal models of electrical machines are fundamental for the design and management of electric powertrains since they allow evaluation of multiple drive cycles in a very short simulation time and implementation of model-based control schemes. A common technique to obtain these models involves homogenization of the electrical winding geometry and thermal properties. However, incorrect estimation of homogenized parameters has a significant impact on the accuracy of the model. Since the experimental estimation of these parameters is both costly and time-consuming, authors usually prefer to rely either on simple analytical formulae or complex numerical calculations. In this paper, we derive a low-order homogenized model using the method of multiple-scales (MS) and show that this gives an accurate steady-state and transient prediction of hot-spot temperature within the windings. The accuracy of the proposed method is shown by comparing the results with both high-order numerical simulations and experimental measurements from the literature.

FINITE ELEMENT TECHNIQUE FOR SOLUTION OF THERMO-CONTACT PROBLEMS AND ITS APPLICATION IN NUMERICAL ANALYSIS OF DEVICES WORKING WITH INDUCTION HEATING

Purpose. To develop an effective approach for the numerical solution of transient thermo-contact problems and present a typical example of its utilization regarding devices working on the principle of thermoelasticity produced by induction heating and specific technological processes intended for assembly and disassembly of systems containing shrink fits. Methodology. A finite element technique for solution of 2D multiphysics (electromagnetic, thermal and structural) problems is developed, taking into account temperature dependences of material properties and continuous variations of the contact surfaces. Modeling of the contact interaction between two parts is based on the concept of a special contact finite element having no thickness. The functional for the temperature problem is supplemented with components corresponding to the thermal conductivity of this contact layer. The heat generated due to mutual sliding of both parts can also be taken into account, but the heat capacity (specific heat) of the contact layer is neglected. Using a special 1D 4-node finite elements a system of equations for the description of the thermo-contact problem is obtained. Originality. Relatively simple analytical formulae for calculation of the contact thermal resistances occurring in specific parts of electrical machines are known. The paper offers an alternative approach for the numerical solution of transient thermo-contact problems based on the concept of a special 1D contact finite element having no thickness. Results. The presented technique is applied for the computer simulation of assembly and disassembly of a shrink fit using induction heating. Conclusions regarding the choice of technological modes are made. Comparative computations for drills made from hard alloy and alloyed tool steel are carried out.

Structural and Electronic Properties of Graphdiyne Carbon Nanotubes from Large-Scale DFT Calculations

Using large-scale DFT calculations, we have investigated the structural and electronic properties of both armchair and zigzag graphdiyne nanotubes as a function of size. To provide insight in these properties, we present new detailed calculations of the structural relaxation energy, effective electron/hole mass, and size-scaling of the bandgap as a function of size and chirality using accurate screened-exchange DFT calculations. These calculations provide a systematic evaluation of the structural and electronic properties of the largest graphdiyne nanotubes to date - up to 1,296 atoms and 23,328 basis functions. Our calculations find that zigzag graphdiyne nanotubes (GDNTs) are structurally more stable compared to armchair GDNTs of the same size. Furthermore, these large-scale calculations allow us to present simple analytical formulae to guide future experimental efforts for estimating the fundamental bandgaps of these unique nanotubes as a function of chirality and diameter. While the bandgaps for both the armchair and zigzag GDNTs can be tuned as a function of size, the conductivity in each of these two different chiralities is markedly different. Zigzag GDNTs have wider valence and conduction bands and are expected to have a higher electron- and hole-mobility than their armchair counterparts.

The tennis racket effect in a three-dimensional rigid body

We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip (π- rotation) of the head of the racket when a full (2π) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.

State dependence of Rydberg interaction-induced collisional loss

We present a simple analytical formula from an existing theoretical model and theoretically investigate in detail the state dependence of interaction-induced collisional loss rate coefficients, and the various parameter effects on collisional loss rate. We also investigate the different mechanisms and corresponding effects on collisional loss by analyzing our previous experimental results using the present formula, and even investigate the time evolution of Rydberg atom number for different Rydberg states.

Laser heating of dielectric particles for medical and biological applications.

We consider the general problem of laser pulse heating of a spherical dielectric particle embedded in a liquid. The discussed range of the problem parameters is typical for medical and biological applications. We focus on the case, when the heat diffusivity in the particle is of the same order of magnitude as that in the fluid. We perform quantitative analysis of the heat transfer equation based on interplay of four characteristic scales of the problem, namely the particle radius, the characteristic depth of light absorption in the material of the particle and the two heat diffusion lengths: in the particle and in the embedding liquid. A new quantitative characteristic of the laser action, that is the cooling time, describing the temporal scale of the cooling down of the particle after the laser pulse is over, is introduced and discussed. Simple analytical formulas for the temperature rise in the center of the particle and at its surface as well as for the cooling time are obtained. We show that at the appropriate choice of the problem parameters the cooling time may be by many orders of magnitude larger the laser pulse duration. It makes possible to minimize the undesirable damage of healthy tissues owing to the finite size of the laser beam and scattering of the laser radiation, simultaneously keeping the total hyperthermia period large enough to kill the pathogenic cells. An example of application of the developed approach to optimization of the therapeutic effect at the laser heating of particles for cancer therapy is presented.

Analysis of Collisional Cross Sections of Rydberg nS and nD States of Ultracold Caesium Atoms

We present a simple analytical formula derived from an existing theoretical model and a detailed theoretical investigation of effects of the van der Waals interaction and dipole–dipole interaction on collisional cross sections as functions of various parameters. We analyze the main mechanism leading to large collisional cross sections on the basis of our previous experimental results using the present formula and also analyze the effects of some other factors on collisional cross sections.

Simple J-factors and D-factors for indirect dark matter detection

J-factors (or D-factors) describe the distribution of dark matter in an astrophysical system and determine the strength of the signal provided by annihilating (or decaying) dark matter respectively. We provide simple analytic formulae to calculate the J-factors for spherical cusps obeying the empirical relationship between enclosed mass, velocity dispersion and half-light radius. We extend the calculation to the spherical Navarro-Frenk-White (NFW) model, and demonstrate that our new formulae give accurate results in comparison to more elaborate Jeans models driven by Markov Chain Monte Carlo methods. Of the known ultrafaint dwarf spheroidals, we show that Ursa Major II, Reticulum II, Tucana II and Horologium I have the largest J-factors and so provide the most promising candidates for indirect dark matter detection experiments. Amongst the classical dwarfs, Draco, Sculptor and Ursa Minor have the highest J-factors. We show that the behaviour of the J-factor as a function of integration angle can be inferred for general dark halo models with inner slope $\gamma$ and outer slope $\beta$. The central and asymptotic behaviour of the J-factor curves are derived as a function of the dark halo properties. Finally, we show that models obeying the empirical relation on enclosed mass and velocity dispersion have J-factors that are most robust at the integration angle equal to the projected half-light radius of the dSph divided by heliocentric distance. For most of our results, we give the extension to the D-factor which is appropriate for the decaying dark matter picture.

Entanglement dynamics of the ultrastrong-coupling three-qubit Dicke model

We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regimes. Qualitative differences arise when comparing to the single- and two-qubit systems - simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for the qubit-field and qubit-qubit entanglement inside the three-qubit system in the ultra strong coupling regime, and the resistance to the sudden death proves the robustness of the GHZ state.

Error Probability Analysis and Applications of Amplitude-Coherent Detection in Flat Rayleigh Fading Channels

This paper presents the detector design and symbol error rate (SER) analysis of $M$ -ary amplitude shift keying over multipath fading channels using amplitude-coherent detection (ACD). The optimum detector is derived using the maximum likelihood criterion, and then it is used to derive two efficient low-complexity suboptimal detectors. The probability distribution function of the decision variables and the SER of the two suboptimal detectors are expressed using simple closed-form analytical formulas when single receiving antenna is used. The SER with receiver diversity is obtained using Monte Carlo simulation. The obtained analytical and simulation results reveal that ACD can provide reliable SER as compared with noncoherent detection. Moreover, we present an efficient blind channel estimation algorithm using ACD and hybrid modulation frame structures.

Simple analytical algorithm for constructing the envelope of the projectile trajectories in midair

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. The air drag force is taken into account asthe quadratic resistance law.An analytic approach is used for the investigation. Simple analytical formulae are used for constructing the envelope of the family of the projectile trajectories. The equation of envelope is applied for the determination of the maximum range of flight. The motion of a baseball is presented as an example.

Multiscale adaptive inference on conditional moment inequalities

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple analytic formula, and to prove the asymptotic validity of a modified bootstrap procedure. The asymptotic distribution is extreme value, and the proof uses new techniques to overcome several technical obstacles. The test detects local alternatives that approach the identified set at the best rate among available tests in a broad class of models, and is adaptive to the smoothness properties of the data generating process. Our results also have implications for the use of moment selection procedures in this setting. We provide a Monte Carlo study and an empirical illustration to inference in a regression model with endogenously censored and missing data.