Potential Equation Research Articles

Development of a Simple and Robust Kinetic Model for the Production of Succinic Acid from Glucose Depending on Different Operating Conditions

Succinic acid (SA) is one of the main identified biomass-derived chemical building blocks. In this work we approach the study of its production by Actinobacillus succinogenes DSM 22257 from glucose, focusing on the development and application of a simple kinetic model capable of representing the evolution of the process over time for a great diversity of process variables key to the production of this platform bio-based chemical: initial biomass concentration, yeast extract concentration, agitation speed, and carbon dioxide flow rate. All these variables were studied experimentally, determining the values of key fermentation parameters: titer (23.8–39.7 g·L−1), yield (0.59–0.72 gSA·gglu−1), productivity (0.48–0.96 gSA·L−1·h−1), and selectivity (0.61–0.69 gSA·gglu−1). Even with this wide diversity of operational conditions, a non-structured and non-segregated kinetic model was suitable for fitting to experimental data with high accuracy, considering the values of the goodness-of-fit statistical parameters. This model is based on the logistic equation for biomass growth and on potential kinetic equations to describe the evolution of SA and the sum of by-products as production events that are not associated with biomass growth. The application of the kinetic model to diverse operational conditions sheds light on their effect on SA production. It seems that nitrogen stress is a good condition for SA titer and selectivity, there is an optimal inoculum mass for this purpose, and hydrodynamic stress starts at 300 r.p.m. in the experimental set-up employed. Due to its practical importance, and to validate the developed kinetic model, a fed-batch fermentation was also carried out, verifying the goodness of the model proposed via the process simulation (stage or cycle 1) and application to further cycles of the fed-batch operation. The results showed that biomass inactivation started at cycle 3 after a grace period in cycle 2.

Large amplitude electrostatic solitary waves in anisotropic plasma

The propagation of nonlinear ion-acoustic solitary waves (IASWs) is investigated in a magnetized anisotropic electron ion plasma with Cairns distributed electrons. The ions are warm and exhibit pressure anisotropy due to the external magnetic field. The energy integral equation for the wave potential is derived via Sagdeev approach. The effect of various physical plasma parameters (nonthermality, ion pressure anisotropy) on the characteristics of IASWs is investigated in detail. The present investigation could be of interest to space and astrophysical plasma systems having ion pressure anisotropy, for instance, in the magnetosphere and near earth magnetosheath.

Linear Thermal Expansion and Specific Heat Capacity of Cu-Fe System Laser-Deposited Materials

The coefficient of linear thermal expansion and the specific heat capacity of laser-deposited Cu-Fe alloys fabricated from tin, aluminum, chromium bronze (89–99 wt.% Cu), and SS 316L were studied. The investigated alloys had a 1:1 and a 3:1 bronze–steel ratio. The Al–bronze-based alloy showed the lowest value of linear thermal expansion coefficient: (1.212 ± 0.095)∙10−5 K−1. Contrarily, this value was the highest {[(1.878–1.959) ± 0.095]∙10−5 K−1} in the case of functionally graded parts created from alternating layers of bronze and steel. Differential scanning calorimetry provided experimental results about the specific heat capacity of the materials. In the case of Al–bronze-based specimens, it demonstrated a decrease in the specific heat capacity until ~260 °C and its further increase during a heating cycle. Exothermic peaks related to polymorphic transformations were observed in the Al–bronze-based specimens. Cooling cycles showed monotonous behavior for specific heat capacities. It had exothermic peaks in the case of Cr–bronze-based alloys. A Lennard-Jones potential equation was used for testing the relation between heat capacity and thermal expansion. A three-way interaction regression model validated the results and provided the relative thermal expansion of commercially pure DED-fabricated SS 316L. Its specific heat capacity was also studied experimentally and was 15–20% higher in comparison to the traditional method of production.

Insights into seasonal-variability of SVOCs, morpho-elemental and spectral characteristics of PM2.5 collected at a dense industrial site: Faridabad, Haryana, India

The development-oriented anthropogenic activities have led to intensive increase in emission of various organic pollutants, which contribute considerably to human health risk. In the present study, chemical, physical and spectral characterisation of fine particulate matter (PM2.5), collected at Faridabad city, in northern India, were examined. Seasonal variation of organic compounds [n-alkanes, polyaromatic hydrocarbons (PAHs) and phthalic acid esters (PAEs)], and potential health risk of Polyaromatic hydrocarbons (PAHs) exposure using toxic equivalency potential (TEQ) approach had been assessed. These showed seasonal average values ranging from 156.4 ± 57.0 ng/m3 to 217.6 ± 72.9 ng/m3, 98.0 ± 21.4 ng/m3 to 177.8 ± 72.8 ng/m3, and 30.9 ± 11.9 ng/m3 to 82.5 ± 29.2 ng/m3, respectively, with the highest value for winter. It is noteworthy that unlike, n-alkanes and PAEs, PAHs were least during spring. The high molecular weight PAHs (BaP, BkF, DahA and IcdP) were found to exhibit higher TEQ values (ranging from 0.7 to 9.7) despite of their lower concentrations. The PAH diagnostic ratio, carbon preference index and total index revealed the enhanced impact of biogenic sources of emissions in comparison to diesel emission sources during winter.

Homogenization of ferrofluid flow models in porous media with Langevin magnetization law

The paper is concerned with the homogenization of the equations describing the flow of a ferrofluid through a heterogeneous porous medium Ω in the presence of an applied magnetic field. We discuss two models where the magnetization M is parallel to the magnetic field H. In the first one M and H satisfy the relation M=λ01ΩfH in Ω, where λ0 is a positive constant and 1Ωf is the characteristic function of Ωf (the pore space). In the second model, M and H satisfy the Langevin magnetization law M=MsL(b1|H|)|H|1ΩfH, where L is the Langevin function given by L(x)=1tanh⁡x−1x, Ms is the saturation magnetization and b1 is a positive physical constant. The velocity and the pressure satisfy the Stokes equation with a Kelvin magnetic force. We perform the homogenization of the equations of each of the two models. Using the two-scale convergence method, we rigorously derive the homogenized equation for the magnetic potential and determine the asymptotic limit of the magnetization. Then we rigorously derive a Darcy law.

Equilibria and energy minimizers for an interaction model on the hyperbolic space

We study an intrinsic model for collective behaviour on the hyperbolic space Hn. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction potentials that include Newtonian repulsion. By using the method of moving planes, we establish the radial symmetry and the monotonicity of equilibria supported on geodesic balls of Hn. We find several explicit forms of equilibria and show that one such equilibrium is a global energy minimizer. We also consider more general potentials and utilize a technique used for Rn to establish the existence of compactly supported global minimizers. Numerical simulations are presented, suggesting that some of the equilibria studied here are global attractors. The key tool in our investigations is a family of isometries of Hn that we have developed for this purpose.

Existence and propagation characteristics of ion-acoustic Kadomtsev–Petviashvili (KP) solitons in nonthermal multi-ion plasmas with kappa distributed electrons

The dynamics of two dimensional Kadomtsev–Petviashvili (KP) electrostatic solitary waves (ESWs) propagating in multi-ion unmagnetized plasma is investigated, in the presence of energetic (nonthermal) electrons. Two distinct ion components are considered as inertial fluids, while inertialess electrons are characterized by an excess superthermal population described by a kappa distribution. The primary (heavier and cold) ion population is assumed to be positively charged, while the charge and sign of the (lighter and warm) ions is left arbitrary in the model. A linear analysis reveals the existence of two harmonic modes propagating with different phase speeds, identified as slow and fast ion-acoustic waves i.e., SIAW, FIAW respectively. Nonlinear analysis, based on a multiscale (reductive perturbation) technique, leads to a two-dimensional Kadomtsev–Petviashvili (KP) equation for the electrostatic potential. Pulse-shaped electrostatic potential solitary wave solutions and associated bipolar electric field structures are obtained analytically as well numerically. A parametric investigation reveals that, if both ion species are positively charged, then either negative or positive polarity electrostatic potential solitary waves structures may occur for the slow (SIAW) mode case (only), depending on the light ion density and temperature. On the other hand, considering a negatively charged light (warm) ion fluid case, then solitary structures of SIAW are formed of positive polarity (only), while their fast counterpart FIAW is of opposite (negative) polarity. The (O, H) multi-ion plasma is considered and parametric dependence of nonlinear electrostatic solitary wave characteristics (amplitude, width) on the intrinsic plasma configurational parameters i.e., light-to-heavy ion density and light ion to electron temperature ratios and nonthermal electrons spectral index kappa is investigated.

A hybrid immersed interface and phase-field-based lattice Boltzmann method for multiphase ferrofluid flow

In this study, we developed a hybrid immersed interface and phase-field lattice Boltzmann (LB) method to simulate multiphase ferrofluid flows. The Laplace equation for the magnetic potential with an interface jump condition was numerically solved using a phase-field-based immersed interface method. The phase interface was tracked by the conservative Allen–Cahn equation. One LB equation was used to capture the interfaces between the two immiscible fluids and another to solve for the hydrodynamic properties. The magnetic stress was treated as an interfacial force at the interface, and thus both the magnetic and capillary forces could be formulated in a unified phase-field method framework. Several typical problems, including a circular cylinder in a uniform magnetic field, deformation of a ferrofluid droplet under a uniform magnetic field, two bubbles merging in the ferrofluid, and a ferrofluid droplet suspension under a shear flow to study the rheological characteristics, were simulated to test the accuracy, applicability, and numerical stability of the present model. The numerical examples demonstrated that the present model is able to capture basic phenomenological features in magnetic multiphase flow problems with high density and high viscosity ratios.

Diffraction of the Field of a Grounded Cable on an Elongated Dielectric Spheroid in a Conducting Layer

Based on a rigorous solution to the problem, analytical expressions are obtained for calculating the diffraction of the electromagnetic field of a grounded cable on an elongated dielectric spheroid in a conductive layer. The field of a grounded AC cable in a conductive layer is determined by solving the Helmholtz equation for the vector potential by using the method of integral Fourier–Bessel transformations, taking into account the boundary conditions at the bottom and surface of the conductive layer. The process of finding the secondary field of an elongated dielectric spheroid on an alternating current in a conducting layer is divided into two stages. First, we find an exact solution to the problem of an elongated dielectric spheroid at a constant current in a homogeneous field, in free space, decomposing this solution into a Taylor series and retaining the first term, which is a dipole approximation. In the second stage, the resulting field as the sum of the fields of the horizontal and vertical dipoles is analytically continued into the frequency domain. The field of the horizontal and vertical dipoles in the conducting layer is obtained by using the method of integral Fourier–Bessel transformations, taking into account the boundary conditions at the bottom and surface of the conducting layer. The resulting solution is presented in a closed form in elementary functions and has an accuracy level acceptable for the practice. Graphs showing the flow characteristics of an elongated dielectric spheroid modeling a swimmer in a light diving suit are given. The influence of the water–air boundary on the increase in the secondary field of the dielectric spheroid, which leads to an increase in the reliability of object detection, is revealed. The practical implementation of the described device protected by a patent and the experimental data of testing the device layout on the Gulf of Finland are given. A good agreement between the theoretical and experimental flow characteristics of a dielectric object both in shape, amplitude, and phase, is revealed.

Generation of vibration load spectrum for fatigue analysis of equipment mounted on bogie frame of railway vehicle based on fatigue damage spectrum

The equipment mounted on the bogie frame of railway vehicles is subjected to non-stationary vibrations from the bogie frame. Currently, the vibration load spectrum for fatigue analysis of equipment is expressed with the power spectral density, which is generally obtained with the power values of measured vibrations or stationary Gaussian vibrations collected at the specific operating conditions. However, this does not have the equivalent damage potential as the non-stationary vibrations. Thus, a generation method of the vibration load spectrum is proposed based on the fatigue damage spectrum (FDS) to obtain the equivalent damage potential as the one from the non-stationary vibrations in this paper. That is, the FDS of non-stationary vibration is calculated with the time domain method, and the vibration load spectrum is generated in the frequency domain with this FDS. Then the method is verified by the measured vibration and dynamic strain of equipment. Finally, the vibration load spectrum of equipment mounted on the bogie frame is generated with the measured vibrations in a maintenance cycle and the fatigue analysis is performed. The results show that the generated vibration load spectrum can validly contain the high power in non-stationary vibrations and express the distribution of power over frequency, which gives much better estimates of the fatigue damage of equipment than other load spectra. The generated vibration load spectrum is suitable for quantifying the actual non-stationary vibrations and can be used for the anti-fatigue design of equipment.

Divergence-Preserving MHD Solutions Using a Noniterative Hyperbolic Conservation Law Scheme

The divergence constraint, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\nabla$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot$</tex-math> </inline-formula> B <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 0, presents a central challenging numerical feature of electromagnetic and magnetohydrodynamic solvers. In general, this constraint is not strictly enforced in hyperbolic solvers and tends to accumulate error over the duration of a simulation, polluting the solution with unphysical behavior. In this article, we present a numerical scheme that constructs a system of hyperbolic conservation laws that already satisfy the divergence constraint, starting from the potential form of Maxwell’s equations and basic derivative relationships. The new system consists only of the first-order spatial differentiation, in contrast to the potential equations which are second order; this allows them to be directly integrated into the existing hyperbolic solvers with no additional implementation changes needed. Furthermore, since the system of conservation laws constructed automatically satisfies the divergence criteria, no subiteration is required to resolve the divergence-free solution. We present the results of integrating this new conservation law approach in an existing finite volume plasmadynamic solver that discretizes the coupled Maxwell and Navier–Stokes equations. Numerical tests indicate that the new approach can strongly resolve physical solutions. The divergence error is also measured and quantified for these problems, showing that the new system suppresses divergence error by many orders of magnitude.

Efficient removal of antibiotic ciprofloxacin by catalytic wet air oxidation using sewage sludge-based catalysts: Degradation mechanism by DFT studies

In this work, the sewage sludge-derived activated carbon (SAC) loaded with iron nanoparticles (FeSAC) showed a highly effective catalytic activity in the degradation of the antibiotic ciprofloxacin by the CWAO reaction. The properties of FeSAC catalyst were studied by using N2 adsorption-desorption measurements at 77 K, scanning electron microscopy, X-ray fluorescence spectroscopy, X-ray photoelectron spectroscopy and thermogravimetric analysis. The CWAO reaction was evaluated at different temperatures (120–140 ºC), total pressure (10–30 bar) and catalyst doses (0.1–0.7 g/L) in a batch reactor. In this regard, temperature and catalyst dosage showed a significant impact on the removal of the tested antibiotic. By using a catalyst dose of 0.7 g/L, ciprofloxacin degradation and CO2 selectivity were higher than 99 % and 60 %, respectively, and were achieved within two hours at 140 °C and 20 bar. The loss of the active phase (Fe) of the catalyst in the reaction medium was measured, obtaining negligible values (less than 24 ppb). This catalyst showed high stability under the tested reaction conditions. In addition, a potential equation was proposed to correctly describe the evolution of ciprofloxacin degradation. The calculated activation energy of the CWAO process was 53.8 kJ/mol. Additionally, Density Functional Theory (DFT) calculations were performed to illustrate the degradation mechanism of ciprofloxacin, where the electronic energies indicated the compounds that are most difficult to degrade by CWAO. Finally, a proof of concept using an environmentally-relevant matrix was carried out, verifying the technical feasibility of the synthesized catalyst for its application with more complex matrices, consecutive reaction cycles and at a low treatment cost.

Brainstem auditory physiology in children with listening difficulties,

Children who have listening difficulties (LiD) despite having normal audiometry are often diagnosed as having an auditory processing disorder. A lack of evidence regarding involvement of specific auditory mechanisms has limited development of effective treatments for these children. Here, we examined electrophysiologic evidence for brainstem pathway mechanisms in children with and without defined LiD. We undertook a prospective controlled study of 132 children aged 6–14 years with normal pure tone audiometry, grouped into LiD (n = 63) or Typically Developing (TD; n = 69) based on scores on the Evaluation of Children's Listening and Processing Skills (ECLiPS), a validated caregiver report. The groups were matched on age at test, sex, race, and ethnicity. Neither group had diagnoses of major neurologic disorder, intellectual disability, or brain injuries. Both groups received a test battery including a measure of receptive speech perception against distractor speech, Listening in Spatialized Noise - Sentences (LiSN-S), along with multiple neurophysiologic measures that tap afferent and efferent auditory subcortical pathways. Group analysis showed that participants with LiD performed significantly poorer on all subtests of the LiSN-S. The LiD group had significantly greater wideband middle ear muscle reflex (MEMR) growth functions in the left ear, and shorter Wave III and Wave V latencies in auditory brainstem responses (ABR). Across individual participants, shorter latency ABR Wave V correlated significantly with poorer parent report of LiD (ECLiPS composite). Greater MEMR growth functions also correlated with poorer ECLiPS scores and reduced LiSN-S talker advantage. The LiD and TD groups had equivalent summating potentials, compound action potentials, envelope-following responses, and binaurally activated medial olivocochlear reflexes. In conclusion, there was no evidence for auditory synaptopathy for LiD. Evidence for brainstem differences in the LiD group was interpreted as increased central gain, with shorter ABR Wave III and V latencies and steeper MEMR growth curves. These differences were related to poorer parent report and speech perception in competing speech ability.

Electromagnetohydrodynamic effects with single-walled carbon nanotubes particles in a corrugated microchannel

Single-walled carbon nanotubes (SWCNTs) are an advanced product of nanotechnology with notable mechanical and physical properties. This motivated us to investigate the effect of electromagnetic hydrodynamic (EMHD) flow on SWCNTs suspended in a microchannel with corrugated walls. The corrugation of the wavy walls is described by periodic sinusoidal waves of small amplitudes ε, either in phase or out of phase. The problem simulated with a system of governing equations, such as potential, momentum, and heat equations, which were solved analytically using the perturbation method. The behavior of nanofluid velocity, temperature, volumetric flow rate, and average velocity was investigated using three models of thermal characteristics. The results confirm that, the addition of SWCNTs, reduces the fluid velocity at the center of the channel by providing resistance to the fluid motion. The concentration ϕ of SWCNTs influence enhances the rate of heat transfer. Additionally, Xue's model has the highest heat transfer rate compared to Maxwell and Hamilton Crosser's (H-C) models. Finally, the obtained flow rate results were compared with previously published data and found to be in good agreement.

A Novel Algorithm of Haze Identification Based on FY3D/MERSI-II Remote Sensing Data

Since 2013, frequent haze pollution events in China have been attracting public attention, generating a demand to identify the haze areas using satellite observations. Many studies of haze recognition algorithms are based on observations from space-borne imagers, such as the Moderate Resolution Imaging Spectroradiometer (MODIS), the Visible Infrared Imaging Radiometer Suite (VIIRS) and the Advanced Himawari Imager (AHI). Since the haze pixels are frequently misidentified as clouds in the official cloud detection products, these algorithms mainly focus on recovering them from clouds. There are just a few studies that provide a more precise distinction between haze and clear pixels. The Medium Resolution Imaging Spectrometer II (MERSI-II), the imager aboard the FY-3D satellite, has similar bands to those of MODIS, hence, it appears to have equivalent application potential. This study proposes a novel MERSI haze mask (MHAM) algorithm to directly categorize haze pixels in addition to cloudy and clear ones. This algorithm is based on the fact that cloudy and clear pixels exhibit opposing visible channel reflectance and infrared channel brightness temperature characteristics, and clear pixels are relative brighter, and as well as this, there is a positive difference between their apparent reflectance values, at 0.865 μm and 1.64 μm, respectively, over bright surfaces. Compared with the Aqua/MODIS and MERSI-II official cloud detection products, these two datasets treat the dense aerosol loadings as certain clouds, possible clouds and possible clear pixels, and they treat distinguished light or moderate haze as possible clouds, possible clear pixels and certainly clear pixels, while the novel algorithm is capable of demonstrating the haze region’s boundary in a manner that is more substantially consistent with the true color image. Using the PM2.5 (particle matter with a diameter that is less than 2.5 μm) data monitored by the national air quality monitoring stations as the test source, the results indicated that when the ground-based PM2.5 ≥ 35 μg/cm3 is considered to be haze days, the samples with the recognition rate that is higher than 85% accounted for 72.22% of the total samples. When PM2.5 ≥ 50 μg/cm3 is considered as haze days, 83.33% of the samples had an identification rate that was higher than 85%. A cross-comparison with similar research methods showed that the method proposed in this study had better sensitivity to bright surface clear and haze areas. This study will provide a haze mask for subsequent quantitative inversion of aerosol characteristics, and it will further exert the application benefits of MERSI-II instrument aboard on FY3D satellite.

Theoretic measure and thermal properties of a standard Morse potential model.

Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space

This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented.

Quantized momentum eigenstates and thermodynamic properties of the Feinberg–Horodecki equation for the time-dependent Wei-Hua oscillator

In this study, we obtained exact solutions of the Feinberg–Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtained the partition function for the system and studied other thermodynamic properties that include vibrational mean momentum ( U), vibrational specific heat capacity ( C), vibrational entropy ( s), and vibrational free momentum ( F) as a signature in the momentum space.

Uniform estimates for the Fisher information of the Landau equation for soft potentials

In this work, under some moment conditions on the initial datum, we prove that the Fisher information is uniformly bounded along the solution to the homogeneous Landau equation for moderate soft potentials −2<γ<0. The proof is mainly based on the energy estimates introduced by Alonso, Bagland and Lods [2], and the regularity estimates for the solutions. As a direct application, we also obtain the propagation of the exponential moments for the gradient of the solutions.

Effect of the Quadric Shear Zonal Flows and Beta on the Downstream Development of Certain Unstable Baroclinic Waves

Many factors are affecting the downstream development of baroclinic waves, among which zonal shear flow is one of the factors that need to be considered. In this paper, the influence of zonal shear flow and <em>β</em> on the downstream development of unstable chaotic baroclinic waves is studied from the two-layer model in a wide channel controlled by quasi-geostrophic potential vorticity equation. Through the obtained Lorentz equation, We concentrated on the influence of zonal shear flow (the second derivative of baseline zonal flow is not zero) on the downstream development of baroclinic waves. In the absence of zonal shear flow, chaotic behavior along feature points would occur, and the amplitude would change rapidly from one feature to another, that is, it would change very quickly in space. When zonal shear flow is introduced, the influence of zonal shear flow on the downstream development of unstable baroclinic waves is examined categorically. And from Lorentz’s final equation, we’re investigating a change in his solution. It is found that the zonal shear flow smoothes the solution of the equation and reduces the instability, and with the increase of zonal shear flow, the stability in space will increase gradually. The second derivative of the zonal shear flow (the quadrical shear flow) therefore has a major influence on the stability of space.