Proportionality Constant Research Articles

Transport coefficient sensitivities in a semi-analytic model for magnetized liner inertial fusion

Performance of magnetized liner inertial fusion (MagLIF) experiments is highly dependent on transport processes including magnetized heat flows and magnetic flux losses. Magnetohydrodynamic simulations used to model these experiments require a choice of model for the transport coefficients, which are the constants of proportionality relating driving terms, such as temperature gradients and currents, to the associated heat and magnetic field transport. The coefficients have been the subject of repeated recalculation using various methods throughout the years. Using a semi-analytic MagLIF model [McBride and Slutz, Phys. Plasmas 22, 052708 (2015)], we compare models for the transport coefficients provided by Braginskii [Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205], Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], Ji and Held [Phys. Plasmas 20, 042114 (2013)], Davies et al. [Phys. Plasmas 28, 012305 (2021)], and Sadler et al. [Phys. Rev. Lett. 126, 075001 (2021)]. The choice of model modifies magnetic-flux losses caused by the Nernst thermoelectric effect and thermal conduction losses. We present simulated results from parameter scans conducted in order to compare the effects of the different models on parameters of interest in MagLIF. In some regions of parameter space, discrepancies of up to 38% are found in integrated quantities like the fusion yield. These results may serve as a guide for experimental validation of the various models, particularly as laser preheat energies and initial axial field strengths are increased on MagLIF experiments.

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

Precise control algorithm of rotational speed of the valve-controlled hydraulic motor under load fluctuating conditions.

The present study focuses on the analysis and design of a novel fuzzy adaptive PID control algorithm, aiming to enhance the speed control accuracy of valve-controlled hydraulic motors under load fluctuating conditions. The method of model identification was adopted to calculate the transfer function of valve-controlled hydraulic motor based on the established hydraulic technology scheme. The chassis of the valve-controlled hydraulic motor is subsequently investigated, and a model for E-grade pavement is constructed using the harmonic superposition method. Through dynamic simulation, the load fluctuation range under two common operating conditions is determined. The fuzzy adaptive PID algorithm was subsequently designed in detail, with the error and its rate of change being considered as input parameters, while the increments of the proportional coefficient, integral constant, and differential constant were regarded as output parameters. Co-simulation data indicate that, compared with the PID algorithm, the average error of the fuzzy adaptive PID algorithm can be reduced by more than 50% and the rise time is reduced by 0.04 seconds. To validate the theoretical analysis, a tracked hydraulic chassis was developed and tested. At an expected speed of 200 rev/min, the average error decreased by 1.68 rev/min, while at an expected speed of 1000 rev/min, the average error reduced by 2.68 rev/min. The designed intelligent control algorithm can effectively improve the control accuracy and stability under load fluctuating conditions.

A novel partition function for elementary particles

Three different partition functions are well-known and described in statistical physics. Here, a novel partition function for the description of intra-particular interactions and with this for the mass of particles is presented below. In statistical physics, three different partition functions are already well-established. These are the microcanonical, the canonical, and the macro-canonical partition functions. Here a fourth, novel partition function is added to these already well-established three. Thereby due to the properties of quantum mechanics and superposition, this novel partition function is of fundamental different nature. According to this concept, the new partition function for particles is first defined. The masses and energies of the elementary particles are then calculated using this novel partition function. The energy of an elementary particle is proportional to the mass on the one hand and to the novel partition function on the other. The constant of proportionality with respect to the new partition function is found to be identical with Rydberg constant and Rydberg energy. The relationships found for the proton, the electron, and the sigma particle are then generalized to all elementary particles.

Mixing and ignition characteristics of laser-induced solid fuel pyrolysis under wide-range variation of crossflow

A theoretical model has been developed to elucidate the thermal initiation laser ignition process of solid fuel. This model comprehensively explores both the heating process of solid fuel and the mixing process of gas-phase pyrolysis gases with crossflow conditions. A two-dimensional transient numerical model has been established and validated through experimental investigations across a spectrum of crossflow fluxes (ranging from 20 to 150 kg/m2/s) and pressures (ranging from 0.15 to 1.83 MPa). The study involves a quantitative analysis of the influence of key macroscopic parameters, including laser energy levels, combustion pressure, and flow rates, on essential mixing characteristics. The solid fuel heating process is segmented into two distinct phases: a preheating phase and a pyrolysis phase, with the latter exhibiting considerably higher heating rates. Notably, a direct linear relationship is observed between the laser energy levels and the rate of heating. It reveals that the dynamics of pyrolysis product mixing are primarily determined by the solid fuel pyrolysis rate and the prevailing crossflow conditions. The dimensionless penetration depth, which measures the extent of pyrolysis product mixing with crossflow, demonstrates an exponential positive correlation with pyrolysis rates and oxidizer flow rates while displaying a negative correlation with combustion pressure. This analysis includes the quantitative determination of proportionality constants and power exponents within the correlations. Finally, the study delves into the intricate interplay between crossflow conditions and the criteria for laser ignition, specifically ignition temperature and the flammable lower limit.

The de Broglie-Einstein-Rosen gravitational wave

de Broglie gravitational waves are solutions of the linearized Einstein's field equations in vacuum, with intriguing properties. They are axially symmetric and have an effective mass, which is responsible for longitudinal effects that are absent in standard gravity waves. Moreover, they represent a classical realization of a form of dynamics proposed for quantum particles by de Broglie one hundred years ago. In this paper we will show that this perturbation field can be obtained, apart from a proportionality constant, in the weak field limit of a particular Einstein-Rosen field, which we call the de Broglie-Einstein-Rosen wave. Some properties of this exact solution are also discussed.

JWST-FEAST: Feedback in Emerging extrAgalactic Star clusTers: Calibration of Star Formation Rates in the Mid-infrared with NGC 628

New JWST near-infrared imaging of the nearby galaxy NGC 628 from the JWST Cycle 1 program Feedback in Emerging extrAgalactic Star clusTers (JWST-FEAST) is combined with archival JWST mid-infrared imaging to calibrate the 21 μm emission as a star formation rate (SFR) indicator at ∼120 pc scales. The Paα (1.8756 μm) hydrogen recombination emission line targeted by FEAST provides a reference SFR indicator that is relatively insensitive to dust attenuation, as demonstrated by combining this tracer with Hubble Space Telescope Hα imaging. Our analysis is restricted to regions that appear compact in nebular line emission and are sufficiently bright to mitigate effects of both age and stochastic sampling of the stellar initial mass function. We find that the 21 μm emission closely correlates with the nebular line emission, with a power law with exponent = 1.07 ± 0.01, in agreement with past results. We calibrate a hybrid SFR indicator using a combination of Hα and 24 μm (extrapolated from 21 μm) tracers and derive the proportionality constant between the two tracers, b = 0.095 ± 0.007, which is ∼3–5 times larger than previous derivations using large regions/entire galaxies. We model these discrepancies as an increasing contribution to the dust heating by progressively older stellar populations for increasing spatial scale, in agreement with earlier findings that star formation is hierarchically distributed in galaxies. Thus, the use of hybrid SFR indicators requires prior knowledge of the mean age of the stellar populations dominating the dust heating, which makes their application uncertain. Conversely, nonlinear calibrations of SFRs from L(24) alone are more robust, with a factor ≲ 2.5 variation across the entire range of L(24) luminosities from H ii regions to galaxies.

Controlling the Period-Bubbling Route to Chaos

We describe the period-bubbling attractors, their generation mechanism and chaos control strategy in nonlinear, unidimensional and two-parameter-dependent discrete maps. A theorem for the occurrence of sequential period-bubbling attractors leading to chaos, is presented. It delineates the role of a geometric parameter in the formation of anti-monotonic periodic sequences of each iterate of such discrete maps. The appearances of different period bubbles in two distinct Gaussian and cubic maps are demonstrated in accordance to the theorem. The delimited chaos through period-bubbling route is suppressed by employing linear density feedback with a proportional constant. The study discloses that the period-bubbling transitional route in unidimensional map cannot be suppressed by adopting constant feedback, which is in contrast to the control of period-doubling route to chaos. In Gaussian and cubic maps, the period-bubbling routes to chaos are gradually collapsed for linear density feedbacks, with the enhancements of the feedback strength parameter k. Interestingly, at [Formula: see text], the feedback-influenced Gaussian map experiences tangent bifurcation and chaos can re-enter into its dynamics through that scenario for [Formula: see text]. The tangent bifurcation in the feedback-affected Gaussian map is explained mathematically. However, no such transitional exchange has been perceived in cubic map, for augmented values of the feedback strength parameter.

Approximation of the Pressure-discharge Curve in Inline Drip Irrigation System

The efficiency of drip irrigation systems depends directly on the uniformity of water discharge from emission devices. Ideally, all emitters should discharge equal amounts of water, but variations occur due to hydraulic and manufacturing factors. This study established the pressure-discharge relationship curve and determined emitter flow variation caused by the hydraulic and the manufacturer’s coefficients of variation for 2 and 4 lph inline emitters. The power exponent and constant of the pressure-discharge curve were determined by measuring the emitter flow rates at operating pressures ranging from 0.2 to 3.0 kg/cm². The emitter flow rates of 100 emitters were measured at an operating pressure of 1.0 kg/cm² to determine the manufacturing coefficient (Vm) and emitter flow variation (qvar(m)). The discharge exponent was found to be 0.46 for both emitter flow rates, with proportionality constants of 0.692 for 2 lph and 1.387 for 4 lph emitters respectively. The results showed a strong correlation between pressure and flow rate, with RMSE values of 0.51 and 0.34 lph, and coefficients of determination of 0.988 and 0.991 for 2 and 4 lph emitters, respectively. High manufacturing precision was indicated by low Vm values of 0.0491 for 2 lph and 0.055 for 4 lph emitters, while qvar(m) values were 0.261 for 2 lph and 0.283 for 4 lph emitters. Total coefficient of variation (Vq) values were 0.1 for 2 lph and 0.14 for 4 lph emitters, with total emitter flow variations (qvar) of 0.29 for 2 lph and 0.39 for 4 lph emitters. The study established the pressure-discharge curve for inline drip irrigation systems, emphasizing the critical relationship between pressure and flow rate. The derived chart from pressure discharge relationship is a valuable tool for estimating emitter flow variation due to hydraulic variation within the same subunit. Precise manufacturing and effective management of hydraulic variations are essential for ensuring uniform water distribution, optimizing drip irrigation systems, and ultimately enhancing crop yield and resource utilization.

Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness

In this paper, a three-dimensional vector field model is proposed, whose dimensions are the Hansen Solubility Parameters: dispersion parameter (δD), polarity parameter (δP), and hydrogen bonding parameter (δH). The vector space that defines the field has the peculiarity of having a dispersion vector with a magnitude of 2 as its base vector, while the polarity and hydrogen bonding vectors have a magnitude of 1. A substance is characterised as a position vector, and the interaction between two substances is determined by calculating the vector difference of both, known as the interaction vector. The interaction among substances may involve solubility, swelling, cracking, surface tension, interface tension, and any physical phenomena where the intermolecular energies of dispersion, polarity or hydrogen bonding come into play. This paper studies free surface energy (surface and interfacial tension). It has been found that free surface energy is directly proportional to the square of the magnitude of the interaction vector. The proportionality constant, τ, is expressed in length units, has a value of 0.025 nm, and does not depend on the chemical nature of the substance or state of matter (solid, liquid or gas). The constant value τ appears universal and aligns with the thickness of interfaces, thereby supporting Guggenheim’s hypothesis. This hypothesis asserts that interfaces possess actual thickness and are not merely mathematical surfaces, as originally postulated by Gibbs. Moreover, it also has been found that the interface thickness, τ, is approximately equal to half of the Bohr radius, a0, which is defined by universal constants. Because the solubility parameters of thousands of substances are known and can be easily determined from their molecular structure, a good approximation of the surface and interfacial tension of any given substance can now be calculated. It has also been found that the contact angles of sessile droplets in three-phased systems can be calculated from the interaction vectors of the implicated substances.

A Methodology to Assess Directional and Spatial Variations of Tensile and Fracture Properties in Fabricated Nuclear Components

In the present study, directional and spatial variations in the mechanical properties are calculated in two nuclear-grade materials. In practice, multiple ASTM standard specimens are tested to measure mechanical properties of any material. The variations obtained in the properties during the tests are generally neglected assuming such variations are due to experimental uncertainties. However, such variations may indicate some degree of anisotropy and spatial inhomogeneity in the material due to component fabrication. In the present study, multiple miniaturized tensile specimens are tested. These specimen materials are taken across the thickness and at different geometrical locations in the two manufactured nuclear-grade components. The experimental load versus displacement data of all the specimens are then used to evaluate stress-strain data and cohesive zone parameters. These parameters are determined for each tested specimen separately to gather variations over the geometries of the components. Subsequently, TPB specimens are analyzed employing these parameters to calculate variations in fracture initiation toughness over the geometry. The key findings of the present work include higher strengths in circumferential direction in comparison to the longitudinal direction for SA333 Gr6 steel. A new equation is developed to correlate the material toughness with the fracture toughness with a proportionality constant of 2.7778 for low-alloy carbon steels. The study showed that directional and spatial variations in Jini are less pronounced in 20MnMoNi55 compared to SA333Gr6 materials. This finding is crucial for safety analyses in nuclear components and indicates that this methodology can be applied more widely across different materials.

Universal wing- and fin-beat frequency scaling.

We derive an equation that applies for the wing-beat frequency of flying animals and to the fin-stroke frequency of diving animals like penguins and whales. The equation states that the wing/fin-beat frequency is proportional to the square root of the animal's mass divided by the wing area. Data for birds, insects, bats, and even a robotic bird-supplemented by data for whales and penguins that must swim to stay submerged-show that the constant of proportionality is to a good approximation the same across all species; thus the equation is universal. The wing/fin-beat frequency equation is derived by dimensional analysis, which is a standard method of reasoning in physics. We finally demonstrate that a mathematically even simpler expression without the animal mass does not apply.

Temperature control strategy for safer and heat-efficient operations in a catalytic flow reactor

A new temperature control strategy for a packed-bed tubular reactor was proposed. Case studies of a highly exothermic 1st-order reaction and an actual 2nd-order reaction were conducted using the computational fluid dynamics software COMSOL Multiphysics® 4.4. Through the simulation, the important factors for reactor temperature control were confirmed, which were the parameters related to heat transfer. Based on the ratio of the heat generation rate to the heat transfer rate, a new dimensionless number was proposed for controlling the temperature increase within an acceptable range in a reactor. Through case studies, the validity of the proposed dimensionless number was confirmed, and an important value of a proportionality constant was derived from the results. Using the proposed dimensionless number, a reactor size can be maximized within an acceptable temperature increase. The results obtained in this study are expected to provide important guidelines for temperature control and maximization of production using flow reactors.

In-situ observations of cloud microphysics over Arabian Sea during dust transport events

The unique in situ measurements of clouds and precipitation within the shallow and deep cumulus over the north-eastern Arabian Sea region during the Indian monsoon are illustrated in this study with a focus on droplet spectral parameters. The observational period showed a significant incursion of Arabian dust and the presence of giant cloud condensation nuclei (GCCN), modifying the cloud and precipitation spectral properties. Warm rain microphysics supported the mixed-phase development in these clouds and exhibited hydrometeors of snow, graupel and large aggregates as part of ice processes. Cloud base droplet number concentration is about 142 ± 79 cm−3 which is one third of the cloud condensation nuclei (CCN) number concentration at 0.2% supersaturation. A rapid broadening of droplet size distribution (DSD) near to the cloud base was noted in contrast to polluted continental clouds. Relationship between the relative dispersion ( ε; the ratio of DSD spectral width ( σ ) to mean radius ( rm )) and liquid water adiabatic fraction (AF) indicates that the entrainment effect has increased relative dispersion significantly (2–3 times larger) in these clouds. Effective radius ( reff ) is found to be proportional to mean volume radius ( rv ) with a proportionality constant ( β ) that varies between 1.0–1.6, depending on the spectral dispersion parameter. Drop size distributions for the small cloud droplets with size range 2–50 μ m and the large drizzle drops (or ice hydrometeors) with size range 100–6400 μ m are parameterized using the gamma function distributions useful for large-scale cloud models.

Experimental Evaluation of Pedestrian-Induced Multiaxial Gait Loads on Footbridges: Effects of the Structure-to-Human Interaction by Lateral Vibrating Platforms.

The introduction of resistant and lightweight materials in the construction industry has led to civil structures being vulnerable to excessive vibrations, particularly in footbridges exposed to human-induced gait loads. This interaction, known as Human-Structure Interaction (HSI), involves a complex interplay between structural vibrations and gait loads. Despite extensive research on HSI, the simultaneous effects of lateral structural vibrations with fundamental frequencies close to human gait frequency (around 1.0 Hz) and wide amplitudes (over 30.0 mm) remain inadequately understood, posing a contemporary structural challenge highlighted by incidents in iconic bridges like the Millennium Bridge in London, Solferino Bridge in Paris, and Premier Bridge in Cali, Colombia. This paper focuses on the experimental exploration of Structure-to-Human Interaction (S2HI) effects using the Human-Structure Interaction Multi-Axial Test Framework (HSI-MTF). The framework enables the simultaneous measurement of vertical and lateral loads induced by human gait on surfaces with diverse frequency ranges and wide-amplitude lateral harmonic motions. The study involved seven test subjects, evaluating gait loads on rigid and harmonic lateral surfaces with displacements ranging from 5.0 to 50.0 mm and frequency content from 0.70 to 1.30 Hz. A low-cost vision-based motion capture system with smartphones analyzed the support (Tsu) and swing (Tsw) periods of human gait. Results indicated substantial differences in Tsu and Tsw on lateral harmonic protocols, reaching up to 96.53% and 58.15%, respectively, compared to rigid surfaces. Normalized lateral loads (LL) relative to the subject's weight (W0) exhibited a linear growth proportional to lateral excitation frequency, with increased proportionality constants linked to higher vibration amplitudes. Linear regressions yielded an average R2 of 0.815. Regarding normalized vertical load (LV) with respect to W0, a consistent behavior was observed for amplitudes up to 30.0 mm, beyond which a linear increase, directly proportional to frequency, resulted in a 28.3% increment compared to rigid surfaces. Correlation analyses using Pearson linear coefficients determined relationships between structural surface vibration and pedestrian lateral motion, providing valuable insights into Structure-to-Human Interaction dynamics.

Statistical Mathematical Analysis of COVID-19 at World Level

Worldwide, statistical data of people infected by COVID-19 has been taken until March 29, 2023, which, when correlated, showed a predictive logistic model. The purpose was to determine the predictive model, which was acceptable, in such a way that the proportionality constant and the correlation and determination coefficients are of great importance to estimating epidemiological and pandemic data; coinciding with what was reported by other authors. Bearing in mind that a mathematical model is a mathematical description through a function or equation of a phenomenon in the real world; whose purpose is to understand infections and make predictions for the future. The stages were: to model the number of people infected as a function of time, formulate, and choose the logistic model, determine the model and obtain mathematical conclusions, and make predictions (estimates) about the number of people infected by COVID-19 worldwide. The logistic model was derived to predict the speed of people infected by COVID-19 and the critical time (tc = 733 days) for which the speed was maximum (1694,7209 infected/day). The Pearson correlation coefficient for the time elapsed (t) and the number of people infected (N) worldwide, based on 32 cases, was r = -0.88; the relationship between time and those infected is real, there is a “very strong correlation” between the time elapsed (t) and the number of people infected (N) and 77.03% of the variance in N is explained by t.

Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study

In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively.

Analysis of a mathematical model with hybrid fractional derivatives under different kernel for hearing loss due to mumps virus

ABSTRACT Genetics, birth defects, some viral diseases, persistent ear infections, medications, loud noises, and age can all cause hearing loss, a global health issue. The mumps are typically the cause of unilaterally acquired sensorineural hearing loss in children. A hybrid fractional operator model employing Constant Proportional Caputo (CPC), Constant Proportional Caputo Fabrizio (CPCF), and Constant Proportional Atangana-Baleanu Caputo (CPABC) in the Caputo sense is developed to investigate mumps induced hearing loss in children. We focused on the region that is positively invariant and well-posed in the suggested model. We assessed the endemic and disease free equilibrium, reproductive number, strength number, and parameter sensitivity, and examined the global stability of the proposed system. The existence, uniqueness, and Hilfer generalized proportional operators for the constant of proportionality of the system’s solutions are demonstrated using fixed-point theorems. We simulated a system of fractional differential equations analytically using the Laplace Adomian Decomposition Method (LADM). This study is important since it is the first to model mumps related hearing loss using a fractional order model based on hybrid fractional operators without a singular kernel. The fractional-order derivative retains the system memory effect, is nonlocal, and outperforms the integer-order derivative in this regard. This sort of study aids medical professionals in diagnosis, treatment planning, and decision-making for mumps induced hearing loss.

Distributed Control of a Vibrating String in Response to Pointwise Force Application

The problem of controlling the vibrations of a string by a discrete applied force is considered. The vibrations of the string are modeled by the linear wave equation and the control is provided by an added force term. The wave equation is solved for controlled and uncontrolled cases with and without control force term. The applied force is chosen to be proportional to string displacement at some specified point. In the controlled case; the wave equation involves a control parameter (gain) and related terms involving the value of the displcement at a single point and a delta function. This makes the equation quite different from the usual wave equation. The problem is solved analytically using a modified (compared to usual wave equation) solution procedure and an equation relating the string eigenfrequencies to the proportionality constant (gain) is derived. This allows the observation of the change in eigenfrequencies with the gain. Finally, examples of uncontrolled and controlled responses are presented, graphically. The results show that the resonances can be avoided by the applied control procedure.

Dynamics of polarization reversal in neodymium-doped PMN-PT ceramic

In this investigation, we present a comparative dynamic scaling analysis of switching and non-switching loops for PMN-PT ceramic and its neodymium-doped counterpart. The results demonstrate that both the samples exhibit similar scaling relations at high fields, suggesting that their distinct piezoelectric behaviour primarily stems from their polarization dynamics at low fields. For E<4kV/cm, the switching polarization for PMN-PT and Nd:PMN-PT follows the scaling relations: <ASW>=1.65*E5.89f−0.27 and <ASW>=34.5*E3.4f−0.2, respectively. On the other hand, non-switching polarization for the two samples follows the relations: <ASW>=2.26*E4.28f−0.15 and <ASW>=65.9*E1.95f−0.05, respectively. These scaling relations suggest that switching as well as non-switching polarization for Nd:PMN-PT respond faster to changing applied field as compared to their PMN-PT counterparts. We argue that the proportionality constants in two scaling relations have significant effect on the electromechanical behaviour of piezoceramics and should be evaluated in forthcoming dynamic scaling investigations. The kinetics of domain reversal, investigated using the Kolmogorov-Avrami-Ishibashi (KAI) model, suggest that the crystallographic domains in both the samples exhibit nucleation limited-switching (NLS) behaviour. We believe that our work will stimulate investigations on other piezoelectrics to corelate their functional response with the underlying dynamics and kinetics of polarization rotation.