Bump Conditions Research Articles

On joint bump conditions for multilinear square functions

On joint bump conditions for multilinear square functions

Sensitivity Analysis of Relative Permeability on Unsteady-State Core Flooding via Experimental Data

The use of computational reservoir simulation plays a key role in understanding fluid flow in geological formations, enabling the development of advanced models and accurate predictions. These simulations rely heavily on parametric constitutive relations to represent essential properties such as relative permeability (Krel), which is required for modeling continuous-scale multiphase flow in porous media. However, the majority of models described in the existing literature contain numerous empirical parameters that must be determined. Regardless of how complex their parameterization is, these parameters have no direct relationship to the problem's underlying physics. As a result, there is a need to estimate these parameters and regularly assess the associated uncertainties. Nevertheless, achieving satisfactory uncertainty quantification requires a preliminary investigation into sensitivity and linear dependence, a step that is often overlooked, especially in the context of core flood experiments. Given this issue, this study aims to analyze the reduced sensitivity coefficient of relative permeability parameters, parameterized using the LET model, in unsteady-state core flooding experiments, considering both bump and no bump conditions, while also taking into account the capillary pressure parameterized via LET. In these experiments, a plug saturated with oil undergoes axial water injection at one end, resulting in oil (and water after breakthrough) being produced at the opposite end. Experimental data includes the pressure difference between the water inlet and the oil (and water) outlet, along with the accumulated volume of produced oil. Based on experimental data, computational simulations were conducted using the Cydar® software to optimize the relative permeability and capillary pressure. The dynamic behavior of the relative permeability parameters' local sensitivity is showcased, alongside their dimensional comparison.

Bump conditions for general iterated commutators with applications to compactness

Bump conditions for general iterated commutators with applications to compactness

Effect of Suspension Preload on Fatigue Life of Two Wheeler Frame

A suspension unit is a significant component in a vehicle. It provides a smooth ride, improves traction, maintains ride geometry and facilitates better handling. A typical suspension setup in a two-wheeler consists of a front and rear suspension setup working independently to achieve the desired function. It connects the wheel to the chassis of the vehicle, transferring road load and hence affecting the durability of the structural members. This research work focuses on the durability aspect of the suspension unit with its preload as the control parameter. A rear suspension with seven preload settings was chosen for this study. The provision requirements of preload settings in suspension were experimentally analyzed using static measurements. The vehicle was instrumented with transducers (strain gauges, accelerometers, linear displacement sensors, and Global Positioning System (GPS) sensors), and dynamic road load data was acquired at different rear suspension preload settings by changing from the minimum, i.e., the 1st setting, to the maximum, i.e., the 7th setting, while keeping other parameters constant. Statistical analysis and fatigue analysis were utilized to study the dynamic effects. It was observed and quantified that increasing the preload for higher static load conditions or rough road conditions provides a smoother ride and improved life due to lower bump stopper engagement and full bump conditions owing to increased compression stroke availability. Keywords: Suspension, Fatigue Life, Stiffness, Riding, Strain Gauges

A sharp two-weight estimate for the maximal operator under a bump condition

A sharp two-weight estimate for the maximal operator under a bump condition

Weighted estimates for square functions associated with operators

AbstractLet L be a non‐negative self‐adjoint operator on . Suppose that the kernels of the analytic semigroup satisfy the upper bound related to a critical function ρ but without any assumptions of smooth conditions on spacial variables. In this paper, we consider the weighted inequalities for square functions associated with L, which include the vertical square functions, the conical square functions and the Littlewood–Paley g‐functions. A new bump condition related to the critical function is given for the two‐weighted boundedness of square functions associated with L. Besides, we also prove the weighted inequalities for square functions associated with L on weighted variable Lebesgue spaces with new classes of weights considered in [5]. As applications, our results can be applied to magnetic Schrödinger operator, Laguerre operators.

Bump conditions and two-weight inequalities for commutators of fractional integrals

This paper gives new two-weight bump conditions for sparse operators related to iterated commutators of fractional integrals. As applications, two-weight bounds for iterated commutators of fractional integrals under more general bump conditions are obtain

Two weight bump conditions for compactness of commutators

We prove two certain weight bump conditions are sufficient for the compactness of the commutator [b, T] where \(b\in CMO\) and T is a Calderón-Zygmund operator. This is the first result for compactness in the two weight setting without additional assumptions on the individual weights.

Cooperative Control of Interconnected Air Suspension Based on Model Predictive Control

The suspension system is a significant part of a vehicle because it transmits the torque and force between the wheels and the frame, meeting the requirements of ride comfort. In this paper, a novel interconnected air suspension was introduced and a cooperative control between interconnected mode activation (IMA) and outsourced mode activation (OMA) was designed. To improve ride comfort in a bus at a minimal energy consumption, this cooperative control based on model predictive control (MPC) for computing the best force and the rule was defined to distribute the best suspension force generated by IMA and OMA. The simulation and experimental results showed that the proposed control strategy significantly improved ride comfort in different conditions. Compared with traditional control in the test vehicle, the RMS of the front-left sprung mass and unsprung vertical acceleration decreased by 24.2% and 14.5%, respectively, under a straight condition; the RMS of the sprung (unsprung) mass vertical acceleration reduced by 22.38% and 15.43%, respectively, under a bump condition.

Two-weight estimates for sparse square functions and the separated bump conjecture

We show that two-weight L 2 L^2 bounds for sparse square functions (uniform with respect to sparseness constants, and in both directions) do not imply a two-weight L 2 L^2 bound for the Hilbert transform. We present an explicit counterexample, making use of the construction due to Reguera–Thiele from [Math. Res. Lett. 19 (2012)]. At the same time, we show that such two-weight bounds for sparse square functions do not imply both separated Orlicz bump conditions on the involved weights for p = 2 p=2 (and for Young functions satisfying an appropriate integrability condition). We rely on the domination of L log ⁡ L L\log L bumps by Orlicz bumps observed by Treil–Volberg in [Adv. Math. 301 (2016), pp. 499-548] (for Young functions satisfying an appropriate integrability condition).

New oscillation classes and two weight bump conditions for commutators

In this paper we consider two weight bump conditions for higher order commutators. Given b and a Calderón–Zygmund operator T, define the commutator $$T^1_bf=[T,b]f= bTf-T(bf)$$ , and for $$m\ge 2$$ define the iterated commutator $$T^m_b f = [b,T_b^{m-1}]f$$ . Traditionally, commutators are defined for functions $$b\in BMO$$ , but we show that if we replace BMO by an oscillation class first introduced by Pérez (J Funct Anal 128(1):163–185, 1995), we can give a range of sufficient conditions on a pair of weights (u, v) for $$T^m_b : L^p(v) \rightarrow L^p(u)$$ to be bounded. Our results generalize work of Cruz-Uribe and Moen (Publ Mat 56(1):147–190, 2012), and more recent work by Lerner et al. (J Funct Anal 281(8):46, 2021). We also prove necessary conditions for the iterated commutators to be bounded, generalizing results of Isralowitz et al. (Commutators in the two scalar and matrix weighted setting. Preprint, 2020. http://arxiv.org/abs/2001.11182 ).

Toeplitz Operators on Weighted Bergman Spaces Induced by a Class of Radial Weights

Suppose that \(\omega \) is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and T1-type conditions, we obtain necessary and sufficient conditions of the positive Borel measure \(\mu \) such that the Toeplitz operator \(T_{\mu ,\omega }:L^p_a(\omega )\rightarrow L_a^1(\omega )\) is bounded and compact for \(0<p\le 1\). In addition, we obtain a bump condition for the bounded Toeplitz operators with \(L^1(\omega )\) symbol on \(L^1_a(\omega )\). This generalizes a result of Zhu in (J Funct Anal 87(1):31-50, 1989).

On separated bump conditions for Calderón-Zygmund operators

We improve bump conditions for the two-weight boundedness of Calderón-Zygmund operators introduced recently by R. Rahm and S. Spencer [Israel J. Math. 223 (2018), pp. 197–204].

Musielak-Orlicz-Bumps and Bloom Type Estimates for Commutators of Calderón-Zygmund and Fractional Integral Operators on Generalized Zygmund Spaces Via Sparse Operators

We study continuity properties for commutators of Calderon-Zygmund and fractional integral operators between generalized Zygmund spaces of L log L type, in the variable exponent setting with different weights. In order to reach this goal we use two different approaches: the first one is related to generalized bump conditions on a pair of weights, allowing us to handle with a wide class of symbol involved with the commutator. The other approaches give Bloom type estimates restricting the class of symbols. The techniques involved in both type of results are related with the theory of sparse domination.

Numerical analysis for the prediction of bump prone conditions: A southern Appalachian pillar coal bump case study

Two miners were fatally injured when a pillar bump occurred during retreat mining in a southern West Virginia coal mine. The mine was operating in the Eagle seam with overmining in the No. 2 Gas and Powellton seams. A coal bump is defined as a sudden and violent failure of coal caused by the release of stored strain energy in the pillar. While significant strides have been made by academia, industry, and regulatory agencies to better understand bump conditions and mitigation techniques, coal bumps represent a long standing, highly site-specific engineering problem in which the exact failure mechanism is not clearly understood. In this case history, a cut-by-cut analysis of retreat mining operations was conducted on the 4 East Main leading up to the pillar bump event. Numerical input parameters were derived from site-specific geologic information and mine geometry for the analysis of pillar stress conditions and energy release using LaModel. An overview of stress conditions in the panel was presented including a precursor event that occurred two crosscuts inby the bump site. The methodology presented in the paper for the evaluation of the fatal bump event can be used for the identification of bump prone conditions prior to development and retreat of a mining area.

Design and Optimization of Formula SAE Suspension system

In automobile industry it is essential to produce the Compact and reliable Suspension system in order to increase the vehicle performance. Also, lot of forces during cornering, acceleration and bump conditions are also applied directly during dynamic condition. This article deals with design of Formula SAE Suspension by considering various loads and their simulation on each component of the system

Two Weight Bump Conditions for Matrix Weights

In this paper we extend the theory of two weight, $A_p$ bump conditions to the setting of matrix weights. We prove two matrix weight inequalities for fractional maximal operators, fractional and singular integrals, sparse operators and averaging operators. As applications we prove quantitative, one weight estimates, in terms of the matrix $A_p$ constant, for singular integrals, and prove a Poincar\'e inequality related to those that appear in the study of degenerate elliptic PDEs.

Design and ANSYS analysis of Components of Wheel Assembly of SAE Car

In automobile industry it is essential to produce the light weight assembly in order to increase the vehicle performance. Also, lots of forces during braking, acceleration and bump conditions are also applied directly during dynamic condition. So, this paper deals with calculation of various loads and their simulation. The FEA result indicates that the upright assembly is able to perform safely in real track condition as per performance requirement.

The perspective of using 3D-modeling in the designing of technological solutions for chassis design

In the modern world 3D-technologies plays an important and significant role in almost every spheres of human life. This is particularly pronounced in industry. Perspectives of using these technologies allow optimizing the production of products of varying complexity, reducing production time and reducing the possibility of defects in the early stages of designing. For the showing the application of 3D modeling its application in vehicle designs considered in this paper. For this purpose a vehicle chassis is designed and then the tension distribution of chassis in the bump condition and its analysis are provided.

Influence of tire stiffness on automotive quarter car suspension system

Quarter car automotive suspension model is the model with two degrees of freedom system, which is used for the analysis of ride comfort and vertical movement of the vehicle. It represents the analysis of vehicle suspension system at any one wheel out of all four wheels; it means the vertical motion of the vehicle body at any one wheel of the vehicle is being analyzed to check the performance. Automotive suspension designs have been always compromise between road handling, road holding and passenger comfort. This paper describes the dynamic model of quarter car automotive suspension system for bump condition prepared in MATLAB using Simulink. The influence of varying values of tire stiffness on vertical acceleration of the vehicle has been discussed in this paper. The results obtained from the simulation of simulink model are used for performance investigation and analysis of the dynamic behavior of the vehicle.