Asymptotic Relations Research Articles

Stock assessment of the mud crab (Scylla olivacea) collected from the terrestrial edge of the Sundarbans mangrove forest, Bangladesh

We estimated mud crab (Scylla olivacea) population parameters to determine recruitment patterns, asymptotic carapace width (CW∞), growth coefficient (k), mortality rate (Z, M, and F), exploitation rate (E) and relationship between body weight and carapace width (BW - CW) in the terrestrial edge of the Sundarbans mangrove forest, Bangladesh. Baited long lines and traps were used to collect crab samples from the terrestrial edge of the mangroves (up to 10 km inside of the Sundarbans mangroves) monthly for a year (Jan 2021–Dec 2021). These CW frequency data were utilized to determine population characteristics. Based on the BW × CW relationship, male S. olivacea crabs increased their BW faster (b = 2.89, R2 = 0.86) than females (b = 2.29, R2 = 0.82). Crabs displayed negative growth allometry, b significantly differed from the isometric growth (b = 3). Both male and female CW∞ was estimated to be 126.00 mm and 113.40 mm, with k values of 0.50 yr−1 and 0.48 yr−1, respectively. The total mortality (Z), natural mortality (M), and fishing mortality (F) of male and female crabs were 1.89 yr−1 and 1.84 yr−1, 0.79 yr−1 and 0.80 yr−1 and 1.10 yr−1 and 1.04 yr−1 respectively. Both sexes were recruited using a bimodal recruitment strategy, with a significant peak from March to June. However, young crabs were present year-round. The virtual population analysis (VPA) shows that males and females are caught at smaller sizes (60–90 mm). The estimated exploitation rate (E) exceeds (0.58 for males and 0.57 for females) the optimum exploitation level (E = 0.50) and E values were close to the projected maximum yield per exploitation rate (Emax = 0.655 for males and 0.647 for females) which indicated over-exploitation of the mud crabs from the territorial edge of the Sundarbans mangrove forest of Bangladesh and hence suggested for proper management.

TIC 441725813: A new bright hybrid hot B subdwarf pulsator with differential core versus envelope rotation

Context. The Transiting Exoplanet Survey Satellite (TESS) performs high-precision photometry over almost the whole sky primarily in search of exoplanet transits. It also provides exquisite data to study stellar variability, in particular for pulsating hot B subdwarf (sdB) stars. Aims. We present a detailed analysis of a new hybrid (p- and g-mode) sdB pulsator, TIC 441725813 (TYC 4427-1021-1), discovered and monitored by TESS for 670 days. Methods. The TESS light curves available for this star were analysed using prewhitening techniques to extract mode frequencies accurately. The pulsation spectrum was then interpreted through methods that include asymptotic period spacing relationships and the identification of rotational multiplets. We also exploited a high signal-to-noise ratio (S/N), low-resolution spectrum of TIC 441725813 using grids of non-local thermodynamic equilibrium (NLTE) model atmospheres to derive its atmospheric parameters. Results. The light curve analysis reveals that frequencies are mostly found in the g-mode region, but several p-modes are also detected, indicating that TIC 441725813 is a hybrid sdB pulsator. We identify 25 frequencies that can be associated with ℓ = 1 g-modes, 15 frequencies corresponding to ℓ = 2 g-modes, and six frequencies characteristic of p-modes. Interestingly, several frequency multiplets interpreted as rotational splittings of deep-probing g-modes indicate a slow rotation period of at least 85.3 ± 3.6 day, while splittings of mostly envelope-probing p-modes suggest a significantly shorter rotation period of 17.9 ± 0.7 day, which implies the core (mainly the helium mantle with possibly the deeper partially mixed helium-burning core that it surrounds) rotates at least 4.7 times slower than the envelope. The radial velocity curves indicate that TIC 441725813 is in a close binary system with a low-luminosity companion, possibly a white dwarf. While elusive in the available TESS photometry, a low-frequency signal that would correspond to a period of ∼6.7 h is found, albeit at a low S/N. Furthermore, we estimate the inclination angle to be ∼60° by two independent means. Conclusions. TIC 441725813 is a particularly interesting sdB star whose envelope rotates faster than the core. We hypothesise that this might be caused by the effects of a tidal interaction with a companion, although in the present case, the presence of such a companion will have to be further investigated. This analysis paves the way towards a more detailed seismic probing of TIC 441725813 using optimisation techniques, which will be presented in a second paper.

Relationship between surfactant content and the properties of microfibrillated cellulose/high density polyethylene composites

AbstractMicrofibrillated cellulose (MFC) was uniformly dispersed in high‐density polyethylene (HDPE) using a large amount of surfactant, and composites were prepared after removing the surfactant at different contents. The structural, morphological, thermal, and tensile properties of these composites were systematically investigated. The results demonstrated an asymptotic relationship between the amount of surfactant removed and the number of removal cycles. A negative linear correlation was observed between the surfactant content and the tensile strength, tensile modulus, and storage modulus at −20 °C of the composites, while a positive linear correlation was found with the loss modulus at −20 °C. Excessive surfactant adversely affected the dispersion of MFC, as well as the mechanical properties and thermal stability of the composites. However, when the surfactant content was below 2.8%, its impact on the composite properties was minimal, and the tensile strength, modulus, and thermal stability of the composites were significantly improved compared to neat HDPE. These findings indicate that surfactant pretreatment is an effective strategy for dispersing MFC in non‐polar polymers, and controlling the surfactant content in the final product can effectively tailor the properties of the resulting composites.Highlights Confirms the relationship between surfactant content and MFC/HDPE composite properties. Surfactant content showed an asymptotic relationship with removal cycles. Surfactant content and mechanical properties exhibited a negative linear correlation. Surfactant content and thermal stability exhibited a negative relationship. Surfactant content had minor impact when below 2.8%.

53 Relationship of Angus yearling bull pulmonary arterial pressure estimates with birth weight, gestation length and growth traits

Abstract Pulmonary arterial pressure (PAP), determines the susceptibility to High Altitude Disease (HAD) of an animal, which causes pulmonary hypertension due to hypoxia. Cattle that reside in elevations greater than 1,500 m are more susceptible to HAD. PAP measures the resistance of blood flow through the lungs and can be used as an indicator of the susceptibility of an animal to HAD. It is estimated that 1.5 million head of cattle are raised in high altitude environments (above 1,500 m) and HAD accounts for 3 to 5% of calf death loss yearly. The objectives of this study were to model the relationship of PAP estimates with birth weight, gestation length and growth traits of developing bulls. PAP estimates were collected from Angus yearling bulls ranging in age from 12 to 18-mo of age from a Montana-based Angus operation (> 1,600 m elevation, 5,400 yearlings/18-mo-old bulls from 2016 – 2023). We hypothesized that the relationship between PAP and performance traits could be described with linear or asymptotic models. We used Akaike’s Information Criterion adjusted for small sample sizes (AICc) to evaluate support for competing models reflecting hypotheses about the effects of bull age at time of testing and performance traits. Models containing an asymptotic relationship between PAP and all measured variables were the best supported from the candidate model sets. Bull age at time of PAP testing was not supported in model selection for any of the performance traits measured. PAP was greater for bulls with greater birth weight (P < 0.01; β = 2.86 ± 0.81; R2marginal = 0.25 %; R2conditional = 0.77 %). PAP was greater for bulls that had greater gestation lengths (P < 0.01; β = 33.74 ± 11.25; R2marginal = 1.40 %; R2conditional = 27.37 %). There were no observed relationships between bull PAP and weaning weight (P = 0.26). PAP was less for bulls that had greater yearling weights (P = 0.04; β = -2.16 ± 1.05; R2marginal = 0.09 %; R2conditional = 0.65 %). In addition, PAP was less for bulls that had greater weaning to yearling gains (P = 0.02; β = -1.21 ± 0.54; R2marginal = 0.12 %; R2conditional = 0.79 %). In summary, PAP was related to birth weight, gestation length, yearling weight, and growth between weaning and yearling; however, these relationships explain very little of the variation of PAP estimates.

Tail variance and confidence of using tail conditional expectation: analytical representation, capital adequacy, and asymptotics

Abstract In this paper, we explore the applications of Tail Variance (TV) as a measure of tail riskiness and the confidence level of using Tail Conditional Expectation (TCE)-based risk capital. While TCE measures the expected loss of a risk that exceeds a certain threshold, TV measures the variability of risk along its tails. We first derive analytical formulas of TV and TCE for a large variety of probability distributions. These formulas are useful instruments for relevant research works on tail risk measures. We then propose a distribution-free approach utilizing TV to estimate the lower bounds of the confidence level of using TCE-based risk capital. In doing so, we introduce sharpened conditional probability inequalities, which halve the bounds of conventional Markov and Cantelli inequalities. Such an approach is easy to implement. We further investigate the characterization of tail risks by TV through an exploration of TV’s asymptotics. A distribution-free limit formula is derived for the asymptotics of TV. To further investigate the asymptotic properties, we consider two broad distribution families defined on tails, namely, the polynomial-tailed distributions and the exponential-tailed distributions. The two distribution families are found to exhibit an asymptotic equivalence between TV and the reciprocal square of the hazard rate. We also establish asymptotic relationships between TCE and VaR for the two families. Our asymptotic analysis contributes to the existing research by unifying the asymptotic expressions and the convergence rate of TV for Student-t distributions, exponential distributions, and normal distributions, which complements the discussion on the convergence rate of univariate cases in [28]. To show the usefulness of our results, we present two case studies based on real data from the industry. We first show how to use conditional inequalities to assess the confidence of using TCE-based risk capital for different types of insurance businesses. Then, for financial data, we provide alternative evidence for the relationship between the data frequency and the tail categorization by the asymptotics of TV.

Spherically symmetric configurations in the quadratic f(R) gravity

We study spherically symmetric configurations of the quadratic f(R) gravity [f(R)=R−R2/6μ2]. In the case of a purely gravitational system, we have fully investigated the global qualitative behavior of all static solutions satisfying the conditions of asymptotic flatness. These solutions are proved to be regular everywhere except for a naked singularity at the center; they are uniquely determined by the total mass M and the “scalar charge” Q characterizing the strength of the scalaron field at spatial infinity. The case Q=0 yields the Schwarzschild solution, but an arbitrarily small Q≠0 leads to the appearance of a central naked singularity having a significant effect on the neighboring region, even when the space-time metric in the outer region is practically insensitive to the scalaron field. Approximation procedures are developed to derive asymptotic relations near the naked singularity and at spatial infinity, and the leading terms of the solutions are presented. We have investigated the linear stability of the static solutions with respect to radial perturbations satisfying the null Dirichlet boundary condition at the center and numerically estimate the range of parameters corresponding to stable/unstable configurations. In particular, the configurations with sufficiently small Q turn out to be linearly unstable. Published by the American Physical Society 2024

The Emergence of Order in Many Element Systems

Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called choose the Leader model.

On partial transposes of unitarily invariant random matrices

In this paper, we compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, the asymptotic freeness relation between the ensembles of random matrices, their transposes and their left and right partial transposes is shown.

Divergence beneath the Brillouin sphere and the phenomenology of prediction error in spherical harmonic series approximations of the gravitational field

The Brillouin sphere is defined as the smallest sphere, centered at the origin of the geocentric coordinate system, that incorporates all the condensed matter composing the planet. The Brillouin sphere touches the Earth at a single point, and the radial line that begins at the origin and passes through that point is called the singular radial line. For about 60 years there has been a persistent anxiety about whether or not a spherical harmonic (SH) expansion of the external gravitational potential, V, will converge beneath the Brillouin sphere. Recently, it was proven that the probability of such convergence is zero. One of these proofs provided an asymptotic relation, called Costin’s formula, for the upper bound, EN , on the absolute value of the prediction error, eN , of a SH series model, VN(θ,λ,r) , truncated at some maximum degree, N=nmax . When the SH series is restricted to (or projected onto) a particular radial line, it reduces to a Taylor series (TS) in 1/r . Costin’s formula is EN≃BN−b(R/r)N , where R is the radius of the Brillouin sphere. This formula depends on two positive parameters: b, which controls the decay of error amplitude as a function of N when r is fixed, and a scale factor B. We show here that Costin’s formula derives from a similar asymptotic relation for the upper bound, An on the absolute value of the TS coefficients, an , for the same radial line. This formula, An≃Kn−k , depends on degree, n, and two positive parameters, k and K, that are analogous to b and B. We use synthetic planets, for which we can compute the potential, V, and also the radial component of gravitational acceleration, gr=∂V/∂r , to hundreds of significant digits, to validate both of these asymptotic formulas. Let superscript V refer to asymptotic parameters associated with the coefficients and prediction errors for gravitational potential, and superscript g to the coefficients and predictions errors associated with gr . For polyhedral planets of uniform density we show that bV=kV=7/2 and bg=kg=5/2 almost everywhere. We show that the frequency of oscillation (around zero) of the TS coefficients and the series prediction errors, for a given radial line, is controlled by the geocentric angle, α, between that radial line and the singular radial line. We also derive useful identities connecting KV,BV,Kg , and Bg . These identities are expressed in terms of quotients of the various scale factors. The only other quantities involved in these identities are α and R. The phenomenology of ‘series divergence’ and prediction error (when r < R) can be described as a function of the truncation degree, N, or the depth, d, beneath the Brillouin sphere. For a fixed r⩽R , as N increases from very low values, the upper error bound EN shrinks until it reaches its minimum (best) value when N reaches some particular or optimum value, Nopt . When N>Nopt , prediction error grows as N continues to increase. Eventually, when N≫Nopt , prediction errors increase exponentially with rising N. If we fix the value of N and allow R/r to vary, then we find that prediction error in free space beneath the Brillouin sphere increases exponentially with depth, d, beneath the Brillouin sphere. Because bg=bV−1 everywhere, divergence driven prediction error intensifies more rapidly for gr than for V, both in terms of its dependence on N and d. If we fix both N and d, and focus on the ‘lateral’ variations in prediction error, we observe that divergence and prediction error tend to increase (as does B) as we approach high-amplitude topography.

Reduced-bias estimation of the extreme conditional tail expectation for Box–Cox transforms of heavy-tailed distributions

Conditional tail expectation (CTE) is a coherent risk measure defined as the mean of the loss distribution above a high quantile. The existence of the CTE as well as the asymptotic properties of associated estimators however require integrability conditions that may be violated when dealing with heavy-tailed distributions. We introduce Box–Cox transforms of the CTE that have two benefits. First, they alleviate these theoretical issues. Second, they enable to recover a number of risk measures such as conditional tail expectation, expected shortfall, conditional value-at-risk or conditional tail variance. The construction of dedicated estimators is based on the investigation of the asymptotic relationship between Box–Cox transforms of the CTE and quantiles at extreme probability levels, as well as on an extrapolation formula established in the heavy-tailed context. We quantify and estimate the bias induced by the use of these approximations and then introduce reduced-bias estimators whose asymptotic properties are rigorously shown. Their finite-sample properties are assessed on a simulation study and illustrated on real data, highlighting the practical interest of both the bias reduction and the Box–Cox transform.

Translocation of two-dimensional active polymers through nanopores using Langevin dynamics simulations.

The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs-1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process.

Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The N-soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.

Dietary Super-Doses of Cholecalciferol Fed to Aged Laying Hens Illustrates Limitation of 24,25-Dihydroxycholecalciferol Conversion

BackgroundOlder humans taking high concentrations of vitamin D3 supplementation for a prolonged time may be at risk of vitamin D toxicity. It is unclear how dietary super-doses (10,000 times greater than the requirement) can affect vitamin D3 status in aged animals. Aged laying hens could be a model to compare vitamin D3 supplementation effects with women in peri- or postmenopausal stages of life. ObjectivesWe investigated the dietary super-dose impacts of cholecalciferol (vitamin D3) on vitamin D3 status in aged laying hens in production. MethodsForty-eight 68-wk-old Hy-Line Brown laying hens were individually housed in cages with 8 hens per dietary treatment for 11 wk. Hens were randomly assigned to 1 of 6 treatment groups of dietary vitamin D3 supplementation and consumed ad libitum. Supplementation concentrations were 400, 800, 7400, 14,000, 20,000, and 36,000 IU D3/kg of feed. At the end of the study, all hens were sacrificed, and tissue samples and feces were collected. Plasma and egg yolk vitamin D3 metabolites, calcium and phosphorus composition of eggshells, ileal digesta, and feces were measured. Duodenal, ileal, liver, and kidney gene expression levels were also measured. ResultsWe observed that increasing dietary vitamin D3 increased plasma vitamin D3 and egg yolk vitamin D3 (P < 0.0001 for both sites). We also observed an increase in plasma 24,25-dihydroxycholecalciferol as dietary vitamin D3 concentrations increased (P < 0.0001). The plasma 25-hydroxycholecalciferol:24,25-dihydroxycholecalciferol ratio exhibited an asymptotic relationship starting at the 14,000 IU/kg D3 treatment. ConclusionsDietary super-doses of vitamin D3 led to greater plasma and egg yolk vitamin D3 concentrations, which shows that aged laying hens can deposit excess vitamin D3 in egg yolk. We suggest future research should explore how 24-hydroxylation mechanisms are affected by vitamin D3 supplementation. Further understanding of 24-hydroxylation can help ascertain ways to reduce the risk of vitamin D toxicity.

Solitons, nonlinear wave transitions and characteristics of quasi-periodic waves for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics and plasma physics

A (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation describing many nonlinear phenomena in fluid dynamics and plasma physics is considered. The N-solitons and breathers are obtained by basing on its Hirota’s bilinear form and taking the complex conjugate condition on parameters of N-solitons. What is more, breathers can be transformed into a series of nonlinear localized waves by the mechanism of breather transformation. Then through the multi-dimensional Riemann-theta function and the bilinear method, the high-dimensional complex three-periodic wave solutions are constructed systematically, which are the generalization of one-periodic wave and two-periodic wave solutions. By a limiting procedure, the asymptotic relations between the quasi-periodic waves and solitons are strictly established. Additionally, a novel analytical method of characteristic line is introduced to analyze statistically the dynamical characteristics of the quasi-periodic waves. The analytical method employed in this paper can be further extended to investigate the other complex high-dimensional nonlinear integrable equations.

Connecting exceptional orthogonal polynomials of different kind

The known asymptotic relations interconnecting Jacobi, Laguerre, and Hermite classical orthogonal polynomials are generalized to the corresponding exceptional orthogonal polynomials of codimension m. It is proved that Xm-Laguerre exceptional orthogonal polynomials of type I, II, or III can be obtained as limits of Xm-Jacobi exceptional orthogonal polynomials of the same type. Similarly, Xm-Hermite exceptional orthogonal polynomials of type III can be derived from Xm-Jacobi or Xm-Laguerre ones. The quadratic transformations expressing Hermite classical orthogonal polynomials in terms of Laguerre ones is also extended to even X2m-Hermite exceptional orthogonal polynomials.

Experimental analysis of the melt fraction - mechanical strength relationship for iron ore sinter analogues

This study examined the strength of sinter analogue tablets for different types of iron ore under varying sintering conditions. A steel tamper was designed to quantify strength based on the percentage of 1 mm retained size after a drop weight test. The study found a linear relationship between total melt fraction M and strength index S quantified by mass fraction of the +1 mm retained size: S=0.88M. Importantly, a relationship was found between the total melt and a combined F factor incorporating the thermodynamic liquid fraction (α, representing sintering conditions) and the mineralogical factor loss on ignition (LOI ratio, β, representing ore types), where F=6.5α+β−1. This factor F was found well correlated the total melt via an asymptotic exponential relationship as M=1−2.6e−F. The results also suggested that, to achieve an acceptable strength of 80% +1 mm for a typical basicity B = 2, a sintering temperature range between 1273 and 1370 °C is required for the LOI range between 1.6% to 10.7% respectively. Finally, an analogous analysis was also carried out which proposed a similar trend between sinter yield obtained in a kilogram-scale by lab-scale studies and the present 0.6-g analogue scale.

Approximate solutions for fuzzy stochastic differential equations with Markovian switching

The fuzzy stochastic differential equations with Markovian switching are considered. First, under the Carath e ´ odory assumptions, the existence and uniqueness theorem for the aforementioned equations is given by means of stopping time techniques, discretization method, and the Gronwall-Bellman inequality. Then the boundedness of the second moment of the solutions for such equations is established. Furthermore, by using the averaging method and stochastic analysis, as well as the Bihari's inequality, this paper mainly demonstrates the asymptotic relationship between the solutions of the original equations and the corresponding averaged equations in terms of mean square and probability. Finally, the theoretical result of the averaging method is illustrated by an example.

Asymptotic scaling relations for rotating spherical convection with strong zonal flows

We analyse the results of direct numerical simulations of rotating convection in spherical shell geometries with stress-free boundary conditions, which develop strong zonal flows. Both the Ekman number and the Rayleigh number are varied. We find that the asymptotic theory for rapidly rotating convection can be used to predict the Ekman number dependence of each term in the governing equations, along with the convective flow speeds and the dominant length scales. Using a balance between the Reynolds stress and the viscous stress, together with the asymptotic scaling for the convective velocity, we derive an asymptotic prediction for the scaling behaviour of the zonal flow with respect to the Ekman number, which is supported by the numerical simulations. We do not find evidence of distinct asymptotic scalings for the buoyancy and viscous forces and, in agreement with previous results from asymptotic plane layer models, we find that the ratio of the viscous force to the buoyancy force increases with Rayleigh number. Thus, viscosity remains non-negligible and we do not observe a trend towards a diffusion-free scaling behaviour within the rapidly rotating regime.

An estimate for the sum of a Dirichlet series on an arc of bounded slope

The article considers the behavior of the sum of the Dirichlet series F(s) = \sum nane\lambda ns, 0 &lt; \lambda n \uparrow \infty , which converges absolutely in the left half-plane \Pi 0, on a curve arbitrarily approaching the imaginary axis — the boundary of this half-plane. We have obtained a solution to the following problem: Under what additional conditions on \gamma will the strengthened asymptotic relation be valid in the case when the argument s tends to the imaginary axis along \gamma over a sufficiently massive set.

Symmetry and asymptotic solutions for a magnetohydrodynamics Darcy–Forchheimer flow with a p-Laplacian operator

Fluid flows under a p-Laplacian operator formulation have been considered recently in connection with the modeling of non-Newtonian fluid processes. To a certain extent, the main reason behind the interest in p-Laplacian operators is the possibility of determining experimental values for the constant p appearing in them. The goal of the present study is to introduce the analysis of solutions of a one-dimensional porous media flow arising in magnetohydrodynamics with generalized initial data under a Lebesgue integrability condition. We present a weak formulation of this problem, and we consider boundedness and uniqueness properties of solutions and also its asymptotic relation with the standard parabolic p-Laplacian equation. Then, we explore solutions arising from classical symmetries (including an explicit kink solution in the p = 3 case) along with asymptotic stationary and non-stationary solutions. The search for stationary solutions is based on a Hamiltonian approach. Finally, non-stationary solutions are obtained by using an exponential scaling resulting in a Hamilton–Jacobi type of equation.