Современные проблемы интеллектуальных систем. Республиканская научно-практическая конференция. Джизак, 18-19 апреля 2025 г.
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MATHEMATICAL MODELING OF THE PROCESS OF DISTRIBUTION OF
HARMFUL SUBSTANCES IN THE ATMOSPHERE, TAKING INTO ACCOUNT THE
DIFFUSION COEFFICIENTS
Nabieva Iroda Sultonovna
PhD doctoral student Digital Technologies and Artificial Intelligence Development
Research Institute
Annotation.
In this study, mathematical modeling was carried out to calculate the diffusion
process of harmful substances in the atmosphere, taking into account diffusion coefficients such
as wind speed, particle size, and temperature.
Keywords:
atmosphere, wind speed, particle size, temperature, advection-diffusion.
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССА
РАСПРОСТРАНЕНИЯ ВРЕДНЫХ ВЕЩЕСТВ В АТМОСФЕРЕ С УЧЕТОМ
КОЭФФИЦИЕНТОВ ДИФФУЗИИ
Аннотация:
В данном исследовании при расчете процесса диффузии вредных
веществ в атмосфере было проведено математическое моделирование с учетом таких
коэффициентов диффузии, как скорость ветра, размер частиц и температура.
Ключевые слова:
атмосфера, скорость ветра, размер частицы, температура,
адвекция-диффузия.
ATMOSFERADA ZARARLI MODDALARNING TARQALISH JARAYONINING
DIFFUZIYA KOEFFITSIYENTLARINI INOBATGA OLIB MATEMATIK
MODELLASHTIRISH
Annotatsiya:
Ushbu tadqiqotda atmosferadagi zararli moddalarning tarqalishida, diffuziya
jarayonini hisoblashda shamol tezligi, zarrachalar o‘lchami va harorat kabi diffuziya
koeffitsentlarini hisobga olgan holda matematik modellashtirildi.
Kalit so‘zlar:
atmosfera, shamol tezligi, zarracha o‘lchami, harorat, adveksiya-diffuziya.
Introduction. When modeling the process of transfer of harmful substances in the atmosphere
the main aspects are considered [1, 448-2, 103-116]: source of pollution, its description, the
presence of natural and artificial obstacles, terrain relief, taking into account the influence of
chemical reactions and changes, physical and mechanical properties during the transfer of harmful
substances into the atmosphere, meteorological conditions, washing away by precipitation, settling
in the soil, on the water surface, etc., the existing base for comparing the impact of motor vehicles
on the urban environment (for example, - per person in terms of compliance with sanitary and
hygienic limits, permissible concentrations).
Mathematical modeling of the distribution of harmful substances in the atmosphere, taking
into account the diffusion coefficients. The advection-diffusion equation is proposed for
Современные проблемы интеллектуальных систем. Республиканская научно-практическая конференция. Джизак, 18-19 апреля 2025 г.
224
monitoring and predicting the process of distribution of harmful substances in the atmosphere. The
numerical method is represented by an explicit finite difference scheme. [3, 303-309, 4, 17-32, 5,
27-40].
(1)
initial and boundary conditions:
(2)
(3)
Here,
is the concentration of harmful substances in the atmosphere,
t
is time,
0
0
0
( ),
( ),
( ),
( ),
( ),
( )
E x
E xL
E y
E yL
E z
E zL
t
t
t
t
t
t
are the concentrations passing through the
boundaries of the considered areas,
, ,
x y z
are coordinates of the system,
, ,
u
w
are the wind
speeds in three directions,
g
w
is the settling velocity of the particles,
is the coefficient of
absorption of harmful substances in the atmosphere,
is the coefficient that organizes the
retention of particles by plant elements,
,
,
x
y
z
D D D
are the diffusion coefficients,
Q
is the source
power,
is the Drak function,
p
d
is the particle diameter.
The results obtained in the software show that in the diffusion process, particle size, wind
speed, and temperature play an important role in atmospheric dispersion. Small particles (1*10
-9
m) remain in the air longer and the concentration spreads rapidly, while large particles (1*10
-7
m)
settle faster under the influence of gravity. Furthermore, particle mobility is observed to increase
at high temperatures and decrease at low temperatures. Wind speed also affects the transport of
pollutants; strong winds accelerate horizontal advection and ensure wider dispersion.
Fig.1
. Changes in the concentration of
harmful particles over time and particle size
u
= 1
m/s
,
v
= 1
m/s
,
w
= 0,2
m/s
,
T
= 30°
C
,
t
= 0.7 h
,
d
p
=1e
-7
m
Fig.2
.
Changes in the concentration of
harmful particles over time and particle size
u
= 1
m/s
,
v
= 1
m/s
,
w
= 0,2
m/s
,
T
= 30°
C
,
t
= 1.3 h
,
d
p
=1e
-9
m
2
2
2
2
2
2
(
)
,
,
,
,
,
,
,
x
p
y
p
z
g
g
p
D T u d
D T v d
D T
u
v
w
w
t
x
x
w
w
d
y
z
Q
y
z
0
0
,
t
0
0
0
0
0
0
0
0
0
,
,
,
,
,
.
x
x
y
y
z
z
ExL
x L
Ex
x
x
x L
x
x
EyL
Ey
y L
y
y
y
y
y L
EzL
z L
Ez
z
z
z L
z
z
x
l
x
l
y
l
y
l
z
t
t
t
t
t
t
l
z
l
Современные проблемы интеллектуальных систем. Республиканская научно-практическая конференция. Джизак, 18-19 апреля 2025 г.
225
Over time, pollutants are actively dispersed in the atmosphere, and their distribution area
expands significantly. Wind speed influences the spread of pollutants. These observations make it
important to take into account meteorological conditions when monitoring and forecasting the
impact of industrial emissions on the atmosphere. The developed mathematical model and
numerical algorithm are an effective tool for analyzing and predicting the distribution of pollutants
in the atmosphere.
References
1. Берлянд М.Е. Современные проблемы атмосферной диффузии и загрязнения
атмосферы. Л.: Гидрометеоиздат, 1975. 448 с.
2. Ложкин В.Н., Медейко В.В. Модели оценки экологического ущерба, применяемые
в Российской Федерации, США и странах ЕС, при государственном регулировании
воздействия транспортных средств на окружающую среду // Информационный бюллетень.
№ 2 (32). «Вопросы охраны атмосферы от загрязнения». 2005. С. 103–116.
3. Ravshanov N., Nabieva I.S., Nasrullayev P.A. 2024. Zararli moddalarni atmosferada
tarqalish jarayonini fizik xususiyatlarini sonli tadqiq qilish. Современное состояние и
Перспективы развития цифровых Технологий и искусственного Интеллекта Сборник
докладов международной научно-технической конференции Бухара, 27-28 сентября –C.
303-309
4. Равшанов Н.1, Набиева И.С. 2024. Математическое моделирование процесса
распространения вредных веществ в атмосфере с учетом температуры, физических и
химических свойств. Международный журнал теоретических и прикладных вопросов
цифровых технологий. № 7(4):27-32.
5. Nabieva I.S. 2025. Numerical modeling of the transport and diffusion of pollutant particles
taking into account airflow characteristics and temperature. Problems of Computational and
Applied Mathematics. 1(63):27-40.
SUST SHAKLLANGAN JARAYONLAR TUSHUNCHASI VA XUSUSIYATLARI
Kabildjanov Aleksandr Sabitovich
“TIQXMMI” Milliy tadqiqot universiteti dotsenti
Pulatov G‘iyos Gofurjonovich
“TIQXMMI” Milliy tadqiqot universiteti assistenti
Annotatsiya:
Mazkur tadqiqot ishi sust shakllangan jarayonlarni asosiy tushunchalarini va
xususiyatlarini tahlil qilishga bag‘ishlangan bo‘lib, unda tibbiy, ijtimoiy va texnologik tizimlarda
uchraydigan jarayonlar, jumladan noaniqlik, ko‘p omillilik va formal modellashtirish
murakkabligi kabilar bayon etilgan.
Kalit so‘zlar:
sust shakllangan jarayonlar, yurak-qon bosimi kasalliklari, ob-havo omillari,
noaniqlik, sun’iy intellekt, ansambl yondashuv.
