Volume 1, 2014 - Issue 1

ISSN(Print): 2377-8091

ISSN(Online): 2377-8083

#### Reading: Study the Dynamics of Vibrational Processes of Water Mineral Metabolism of Plants in Ontogenesis

Citation

Vladimir K. Mukhomorov, Ludmila M. Anikina, Olga R. Udalova; Study the Dynamics of Vibrational Processes of Water Mineral Metabolism of Plants in Ontogenesis, Trends Journal of Sciences Research, Volume 1, Issue 1, September 28, 2018, Pages 28-37, 10.31586/Agrophysical.0101.05

Research Article

Open Access

Peer Reviewed

Article Contents

## Study the Dynamics of Vibrational Processes of Water Mineral Metabolism of Plants in Ontogenesis

Trends Journal of Sciences Research, Volume 1, Issue 1, 2018, Pages 28–37.

https://doi.org/10.31586/Agrophysical.0101.05

Received September 20, 2014; Revised November 21, 2014; Accepted December 20, 2018;
Published December 30, 2018

### Abstract

We analyze the experimental data on the dynamics of water and mineral metabolism of tomato plants by using the methods of spectral analysis. Plants were cultivated under controlled conditions. We have used the various compositions of juvenile analogues of thin-layer soil. It is shown that the composition of the soil analogue significantly affects the dynamics of water-mineral metabolism of plants and plant productivity. It was found that the dynamics of the water and mineral metabolism of plants has a clear oscillatory structure. We have identified the most intense frequencies of this process. It was found that in order to maximize the productivity of plants it is necessary that the process of transpiration should contain simultaneously both high-frequency and low-frequency periodicities. This creates the most favorable environment for the development and functioning of the plant root system. It was shown that vibrations of water metabolism closely connected with the vibrations of the content of chemical elements in plants.

### 1. Introduction

Urgent problem of modern crop production is the creation of new economically sound systems for the ecologically clean production of plant products. Studies 1 aimed at studying the patterns of transformation of mineral, organic-mineral and organic root-inhabited systems (RIS) have shown that under the action of the root systems of plants the artificial RIS, as well as natural agro- and ecosystems aspire to the climax state. These processes involve a change in the entire complex biological processes and as a result of these processes lead to a decrease in plant productivity 2. Intensive cultivation of plants under controlled conditions leads to the enrichment of the RIS by the fine-dyspersated compounds and an excessive content of organic material. Maintaining of RIS under controlled agro-ecosystems (CAES), in the juvenile highly active state as well as the optimization of conditions life support of the roots can be achieved in different ways. Controlling these processes in greenhouses carried out by partial or complete replacement of the RIS through certain time of operation. This is not always economically is justified. We have developed another method for achieving these goals, that is based on the principles of maintaining a given level of fertility of the RIS. The method involves the periodical regeneration either of the RIS or of the RIS and plants. Comprehensive regeneration 4 of the RIS allows us to convert the RIS from the climax status into the juvenile status. Creating a thin-film RIS is accompanied by optimization of their hydrophysical characteristic. This is accomplished by using two or more layers of woven materials in conjunction with plastic film or spanbond 5. To ensure favorable conditions for interaction of the root system of vegetative plants with the surface of the RIS we applied on the tissue surface the thin layers of organ mineral pastes of the different compositions. This principle of creating a thin-layer of soil analogues allowed to develop a series of installations with horizontal placement of roots of vegetative plants 6 and, later, with a vertical placement.

We have developed composition of juvenile thin-layer of the soil analogue, which is a combination of a certain proportion of Cambrian clay, bentonite clay, schungite and sapropel. Clay helps to increase the active surface of contact of the root systems of plants with companion microflora 7. Sapropel is a supplier of the humic substances, amino acids, including aspartic acid, glutamic, and also glycine, alanine and histidine into the nutrient medium of plants. In addition, the sapropel promotes to the high enrichment the trophic medium of plants by macro- and microelements 8. This creates the most favorable environment for the development and functioning of the plant root system.

The purpose of this work is to study the effect of treatment of the RIS with different compositions of TJAS on the dynamics of water and mineral exchange. We investigated the dynamics of content K+, Ca2+, Mg2+, $N{O}_{3}^{-}$, ${P}_{2}{O}_{5}^{}$into tomato plants. Tomato plant cultivated under controlled agroecosystem. Experiment also included examining the influence of the dynamics of water-mineral metabolism on the productivity of tomato plants. Using the methods of spectral analysis, we analyze the structure of the vibrational dynamics of water and mineral metabolism of tomato plants during metabolism of plants.

### 2. Materials and Methods

We cultivated the tomato plants of variety "Ultrabek" in vegetation installation under controlled conditions using TJAS as an analogue of soil. The composition of TJAS includes Cambrian clay, bentonite clay, shung it, and sapropel is in the proportions 1: 1: 0.5: 1.

Installation diagram is given in the following work 9. In the germinators we placed the spunbond covered with TJAS. Next we placed the spunbond on two-layer plane wicks (lavsan and nylon). Tomato seedlings grown invinylcubes ($6×6×6$ cm3).The internal cavity of the cube was laid out with spunbond. The cubes we inflated with components of RIS: broken brick, the sawdust treated with TJAS and the miplast without treatment. Tomato seedlings have grown in vinyl boxes ($6×6×6$ cm3) with the spunbond. In the germinator we used sodium lamps DNaT-400. The intensity of the radiant fluxin the region PAR was 100± 10 W/m2. The duration of the light period was 16 hours per day. In the germinator the air temperature is maintained 25 ± 2°C at day and 22 ± 2°C at night. Relative humidity was 50-60%. These conditions allow us to maintain the life support of roots that close to optimal.

Plants were grown in Knop nutrient solution, with correction of the solution during vegetation. We carried out the watering of the plants twice a day. The rest of the time the flow of moisture to the roots of plants is directed by means of the flat wicks from nutrient solution, which was located at the bottom of the germinator 5. Closed cycleis as follows.Once a week after watering plants we poured off the nutrient solution, which was in the germinator. At this time, we measured the volume of the nutrient solution. Decline of water by transpiration of plants is made up to 30 liters. At the same time, we took samples for the determination of nutrients content, as well as carried out the correction of the nutrient solution. During the vegetation, we fulfilled phenological and biometric observations of water exchange (every day) and the absorption of chemical components by plants (once a week). Harvesting was carried out at the 65 day of growing season. We used the colorimetric method with disulfophenic acid for definition of nitrate 10. Potassium we determined by flamephotometry. Phosphorus we determined by photometric method. Calcium and magnesium, we determined by complexometric method 11.

We used the following variants in the experiment. Variant 1: The fabric and spunbond which was handled by TJAS. Seedlings were placed into broken bricks rubble that was handled by TJAS. In addition, we added the black mulch. Variant 2: The fabric, the spunbond which was handled by TJAS. Seedlings were placed into broken bricks rubble that was handled by TJAS. In addition, we added the white mulch, which was covered with humates and TJAS. Variant 3: The fabric, spunbond which was handled by TJAS. Seedlings were placed into sawdust, which were covered by TJAS. Variant 4: In this variant we used the fabric, spun bond, and clean mulch. Seedlings were place donmicroporous plastic. Fourth variant did not contain an organic and mineral components. Number of plants in each variant of the experiment was equal to 10.

### 3. Results and Discussion

Transpiration plays an important role in the life of the plant and its study is of considerable scientific and practical interest for the purposes of managing productivity of phytocenosis under controlled conditions 12. We have arranged the successive measurements chronologically. The interval between observations is equal to one day (and night). This sequence is defined as a time series. As is well known, the time series are called a discrete sequence of numbers in chronological order, which determines the state of the object at time t.

We performed observations of the dynamics of plant transpiration throughout the plant ontogenesis. The experiment demonstrated the oscillatory nature of transpiration (Figure 1) for all variants.

Figure 1.
Dynamics of transpiration of tomato plants. —♦— variant 1, -- ■ - - variant 2, · · ·· · · variant 3, - · -$×$- · - variant 4.

The objective of the study was, firstly, to ascertain whether there deterministic regular periodicity in the dynamics of water use by plants and, secondly, the statistical confirmation that they are not a fortuitousness. Methods that are used in the theory of one-dimensional time series permit to do this. The experimental conditions also involve the total sublation of external influences on the daily rhythms of the RIS – plant system.

As is known, a regular one-dimensional time series maybe represented as a superposition of harmonic oscillations, which have different amplitude and frequency. Spectral analysis allows us to identify the most significant periodic components of the investigated time series, i.e., thereby determineits structure. Cyclical components of the time series are characterized by periods of relative rise and fall of observations. For the quantitative determination of the harmonic oscillations parameters typically use a decomposition of the dispersion of the time series. Detection of the spectrum structure and the spectral density is performed by using Fourier cosine transform of the function of autocovariance in accordance with the definition of 13:

$f\left({\omega }_{j}\right)=\left(1/2\pi \right)\left[{\lambda }_{0}{c}_{0}+2\sum _{k=1}^{m}{\lambda }_{{}_{k}}{c}_{k}\mathrm{cos}\left({\omega }_{j}k\right)\right]$

The spectrum frequencies are determined as follows: ${\omega }_{j}=j\pi /m$, j = 1, 2, …, m. ck is the autocovariance function, ${\lambda }_{{}_{k}}$ is the lag window. m is the integer specifying the number of frequency bands for which estimated harmonic spectrum. From the spectrum of the time series can be found it structure. This allows us to find the periodicities that dominate in the oscillatory process.

Methods of the spectral analysis of one-dimensional time series are able not only reveal the structure of the time series, but also allows us to establish the similarities and differences of the dynamics of processes for different variants of experiment. In the study of the developing in time natural process the question arises usually, what are its the internal temporal relationships. Successive values of observations yt can be interrelated. For example, the observation at the instant of time t + 1 is determined by the previous observation at the instant of time t. We examine preliminarily the existence of autocorrelation for the time series (Figure 1). For this aim we use the criterion of the Durbin-Watson 13:

$d=\sum _{t=1}^{n-1}{\left({y}_{t+1}-{y}_{t}\right)}^{2}/\sum _{t=1}^{n}{y}_{t}^{2}$

here yt are the values of transpiration of tomato plants (inunitsofliters / plant/day (and night)) at time t, n is the total number of observations. For example, using the definition (2) we obtained the value d = 0.096 for the first variant of experiment. This value is considerably less than the lower table value of criteria Durbin-Watson: dlow = 1.53. The significance level is equal toα = 0.05. This inequality indicates that the sequence of observations contains strong autocorrelation. We can obtain similarly, the values of the Durbin-Watson test for the second, third and fourth variants of experiment: d = 0.121; 0.093; 0.106 <<dlow, respectively. Thus, these variants can also include a strong autocorrelation. As is well known existence of autocorrelation in the sequence of observations significantly distorts conclusion about the relationship between the levels of the time series. Therefore, to establish the true time dependence of the series of observations it is necessary eliminate the autocorrelation. Usually, the main contribution to the non-random, long-term evolution of time series brings the systematic component (a trend) of the series. We can get rid of autocorrelation, if we remove a trend. One way to reveal the trend is to apply the method of the analytical smoothing. This approach is considered as the most advanced method.We shall approximate the trend by using a polynomial dependence. We use the method of successive differences, to find out the minimum degree of the polynomial 13. That is, we are looking for the first, second, etc. of levels difference: ${\Delta }_{t}^{1}={y}_{t}-{y}_{t-1}$, ${\Delta }_{t}^{2}={\Delta }_{t}^{1}-{\Delta }_{t-1}^{1}$, ${\Delta }_{t}^{3}={\Delta }_{t}^{2}-{\Delta }_{t-1}^{2}$, …. The calculation is finished when mean difference becomes much less than the previous mean difference. In this case, the method of successive approximations assumes that the previous difference determines the order of the polynomial. For example, we obtained the following sequence of mean differences for the first variant of the experiment: $\overline{{\Delta }_{t}^{1}}=0.004$, $\overline{{\Delta }_{t}^{2}}=0.014$, $\overline{{\Delta }_{t}^{3}}=0.003$. Hence, we can neglect the third mean difference in comparision with the second mean difference. Consequently, the trend can be described by the polynomial of the second degree:

$\begin{array}{l}{y}_{tr}^{\left(1\right)}\left(t\right)={C}_{1}+{B}_{1}t+{A}_{1}{t}^{2},\text{\hspace{0.17em}}{A}_{1}=-2.6×{10}^{-4},\\ {B}_{1}=0.0155,\text{\hspace{0.17em}}{C}_{1}=0.23\\ {t}_{54;0.05}^{\left(cr\right)}=2.00{F}_{2;54;0.05}^{\left(cr\right)}=3.2.\end{array}$

From the sequence of the inequalities (3) it follows that all the explanatory variables of the polynomial are statistically significant.

Using this method, we get the following equations of the trends for the other of variants of the experiment:

$\begin{array}{l}{y}_{tr}^{\left(2\right)}\left(t\right)={C}_{2}+{B}_{2}t+{A}_{2}{t}^{2},\text{\hspace{0.17em}}{A}_{2}=-5.94×{10}^{-5},\\ {B}_{2}=4.17×{10}^{-3},\text{\hspace{0.17em}}{C}_{2}=0.32\\ {y}_{tr}^{\left(3\right)}\left(t\right)={C}_{3}+{B}_{3}t+{A}_{3}{t}^{2},\text{\hspace{0.17em}}{A}_{3}=-1.16×{10}^{-4},\\ {B}_{3}=4.94×{10}^{-3},\text{\hspace{0.17em}}{C}_{3}=0.41\\ {y}_{tr}^{\left(4\right)}\left(t\right)={C}_{4}+{B}_{4}t+{A}_{4}{t}^{2},\text{\hspace{0.17em}}{A}_{4}=-2.5×{10}^{-4},\\ {B}_{4}=1.37×{10}^{-2},\text{\hspace{0.17em}}{C}_{4}=0.31\end{array}$

The authors of papers 12, 14 studied the dynamics of transpiration of the tomato plants of varieties Ottawa-60 during of the ontogeny. Plants were grown under conditions CAES by the aerohydrolyte method on flat thin-layer of RIS (four variants of the experiment). This independent study also gives the trend, which can be described by a polynomialo f the second degree. This indicates the similarity of the deterministic long-term mechanisms of the transpiration of tomato plants.

Thus, the systematic component of long-term dynamic process points that for all analogs of soil are observed increase in plant transpiration in phases of budding, flowering and early fruit set and then the transpiration is decreased in the beginning phase of fruit ripening. The duration of the deterministic growth of water consumption is varied for each variant of the experiment. From equations (3) and (4) it follows that the maximum of trend for the third variant lies at time-domain ~ 21 day (and night). This corresponds to the shortest time interval of all variants. The greatest length of time for which the trend reaches a maximum corresponds to the second variant of the experiment and is equal to ~ 35 days. For other variants of the experiment the trends maximum lies in the time domain between these points of time.

To find the regular short-term oscillations in the vicinity of the trend in the framework of additive model we need to subtract the trend of the original time series: ${\epsilon }_{t}^{\left(i\right)}={y}_{t}^{\left(i\right)}-{y}_{tr}^{\left(i\right)}\left(t\right)$; numbers of the variant are i = 1, 2, 3, 4. The numbers ${\epsilon }_{t}^{\left(i\right)}$are called the remainders of the time series. For example, mean sum of the deviations from trend${\epsilon }_{t}^{\left(1\right)}$ is very little for variant 1. Mean sum is equal to$\sum _{t=7}^{62}{\epsilon }_{t}^{\left(1\right)}{n}^{-1}=0.0005$. Other variants of the experiment also satisfy these conditions.

We verify the remainders to presence of the autocorrelation. For the remainders the criterion of Durbin-Watson is equal to d = 1.91 (variant 1), i.e., greater than the upper tabulated value dup = 1.60. Consequently, series of the remainders ${\epsilon }_{t}^{\left(1\right)}$ can be considered as a time series without autocorrelation and approximation of the trend is adequate. Such time series can be represented as a sum of harmonic oscillations with a certain set of frequencies and amplitudes. d values for the second, the third and the fourth variants are also greater than the upper tabulated value: 1.78; 1.81; 1.69 >dup, respectively.

Figure 2.
Oscillations of the remainders. - ž - ž - ž variant 2, ——— variant 4.

We'll examine whether the oscillations are independent and random or the oscillations are similar and they have common qualitative features (but not in a quantitative sense). For this purpose we use the method of pairwise comparison of qualitative characters. Figure 2 shows comparative dynamics of the remainders for the second and the fourth variants:${\epsilon }_{t}^{\left(2\right)}$ and ${\epsilon }_{t}^{\left(4\right)}$.

For the alternative qualitative characters we choose the positions of the maximum and the minima of ${\epsilon }_{t}^{\left(i\right)}$ with respect to the horizontal axis. We construct the two-by-two table of frequency conjugation for a distribution of maxima and minima of the remainders. Each quadrant of the table contains a certain number of points qij. q11 are the frequencies of the like-sign (positive) deviation of the remainders from the x-axis for the two compared variants; q22 are the frequencies of the like-sign (negative) deviation of the remainders from the x-axis for the two compared variants; q12 are frequencies of negative deviations of the remainders from the x-axis of one variant, at simultaneous positive deviations of the remainders of another variant; q21 are the frequencies of positive deviations of the remainders from the x-axis of one variant, at simultaneous negative deviations of remainders of another variant. For example, we obtained the following frequencies for variants 2 and 4 (Figure 3): q11 = 16 (the right upper quadrant), q22 = 26 (the lower left quadrant), q12 = 6 (the left upper quadrant), q21 = 8 (the right lower quadrant).

Figure 3.
The frequency table of conjugation vibrations of the remainders. Variants of 2 and 4

Using frequencies qij, we can estimate the association coefficient of Yule, which quantitatively determines the closeness of these variants:

$\Phi =\frac{{q}_{11}{q}_{22}-{q}_{12}{q}_{21}}{{q}_{11}{q}_{22}+{q}_{12}{q}_{21}}=0.79$

The coefficient of association $\Phi$ indicates the similarity of the oscillatory processes for variants 2 and 4. Verification of statistical significance of the coefficient $\Phi$ is done using Pearson's test:

$\begin{array}{l}{\chi }^{2}=\frac{n{\left[\left({q}_{11}{q}_{22}-{q}_{12}{q}_{21}\right)-n/2\right]}^{2}}{\left[\left({q}_{11}+{q}_{12}\right)\left({q}_{22}+{q}_{21}\right)\left({q}_{11}+{q}_{21}\right)\left({q}_{22}+{q}_{12}\right)\right]}\\ =10.8>{\chi }_{1;0.05}^{2\left(cr\right)}=3.84\end{array}$

here $n={q}_{11}+{q}_{12}+{q}_{22}+{q}_{21}$. The statistical test (6) confirms that the variants 2 and 4 are similar to each other and have statistically significant qualitative similarity, although quantitative differences naturally exist. Obviously, the observations are not the set of independent and random values, i.e., the time sequences have a deterministic structure. The remainders follow to the rule of the normal distribution. Indeed, the Kolmogorov criteria are as follows: $\lambda$= 0.69 and 0.83 for the second variant and for the fourth variant, respectively. These values are much smaller than the tabulated value ${\lambda }_{0.2}^{\left(cr\right)}$=1.07. This value we choose, in accordance with the recommendation 15 for a very strong level of significance p = 0.2.

For more information about the non-randomness and the qualitative proximity of the two stationary oscillations we can obtain using the unconditional or marginal sample values: ${p}_{ij}={q}_{ij}/n$. They define a measure of a priori realizability of the events. For example, for completely different processes proportion of ${p}_{22}={q}_{22}/n=0.464$ should be very close 16 to the product of the proportions: ${P}_{22}=\left({p}_{12}+{p}_{22}\right)\left({p}_{21}+{p}_{22}\right)$. However, the last product of the proportions ${P}_{22}$ is equal to 0.347, which is markedly different from the proportion of ${p}_{22}$. In this case, the hypothesis of the qualitative distinction of compared variants is rejected. The degree of confidence to the hypothesis about a qualitative similarity of the processes is so much the better, then greater the difference of $\Delta p=|{p}_{ij}-{P}_{ij}|$. We obtain similar result if we choose positions in quadrant i = 1 and j = 1. Pearson criterion 16 is also satisfied to estimation the significance of differences of proportions $\Delta p$. Thus, the dynamics of remainder oscillations is not random for variants 2 and 4, and regularly repeated in time. Consequently, we can consider these oscillations of the remainders as regular (deterministic) and qualitatively similar. We can make similar conclusions about the similarity at the comparison of variants 2 and 3 or 3 and 4, although, of course, there are quantitative differences. That is, for these variants exist stable and qualitatively similar deviations from the trend. Therefore, we can assume the presence at the dynamics of water consumption by plants the regular oscillatory processes that are caused by the mechanism of transpiration. Table 1 demonstrates the statistical characteristics of pair wise comparisons for all variants of the experiment.

Table 1. Statistical characteristics of pairwise comparison of the variants

At the same time, if we compare the intensity of water consumption for the variants 1 and 3, 1 and 2 or 1 and 4, we find that these pairs of the variants qualitatively differ from each other. For example, we obtain close values (position in quadrant i = 2 and j = 2) of the proportions ${p}_{22}$ and ${P}_{22}$ which are equal to 0.357 and 0.315 for the variants 1 and 3, respectively. Therefore, we can‘t consider these variants as qualitatively similar. Indeed, this result is confirmed by the statistical characteristics of Table 1.

Thus, we have found from data of the tables of conjugation there are qualitatively similar of dynamics for the remainders of the following pairs of the variants: the second and the third, the second and the fourth, the third and the fourth. At the same time, the first variant of the experiment has no statistically significant similarity with other variants. Possible reasons for this distinction will be discussed below.

We now define the most significant harmonic periodicities for the residuals, i.e., the intensity of the vibrations, the length of the period and the number of the periodicities for each variant of the analogue of soil. In the Eq. (1) we use the Parzen’s representation for estimates of the lag window values ${\lambda }_{k}$ (weight of auto covariance function):

${\lambda }_{k}=\left\{\begin{array}{l}1-\frac{6{k}^{2}}{{m}^{2}}+\frac{6{k}^{3}}{{m}^{3}},\underset{}{}при\underset{}{}0\le k\le \frac{m}{2};\\ 2{\left(1-\frac{k}{m}\right)}^{3},\underset{}{}при\underset{}{}\frac{m}{2}+1\le k\le m.\end{array}$

We can compute the intensity (power) ${U}_{j}$ of series spectrum by using the following equation 13:

${U}_{j}=\frac{{c}_{0}}{2\pi }+\frac{1}{\pi }\left(\begin{array}{l}\sum _{k=1}^{m/2}{\lambda }_{k}{c}_{k}\mathrm{cos}\left(\frac{\pi k}{m}j\right)\\ +\sum _{k=1+m/2}^{m}{\lambda }_{k}{c}_{k}\mathrm{cos}\left(\frac{\pi k}{m}j\right)\end{array}\right)$

Expansion in series (8) allows us to bring to light the cyclical components that dominate in the dynamics of the process transpiration of tomato plants. For estimates of the spectrum we take the value of m is equal to 28. The larger the value m, the more points in the estimated spectrum. The values of the autocovariance function ${c}_{k}$ are defined as follows:

${c}_{k}=\frac{1}{n}\sum _{t=1}^{n-k}\left({\epsilon }_{t}-\stackrel{_}{\epsilon }\right)\left({\epsilon }_{t+k}-\stackrel{_}{\epsilon }\right)$

here$\stackrel{_}{\epsilon }$ is the central tendency of the remainders.

As is well known, the spectral analysis solves the problem of determining the main powers inusoids that characterize the general laws of the evolution of oscillatory processes. The peak of the most intense component of the spectrum (Figure 4) corresponds to the maximum value of Uj, moreover the determinate harmonic component has a period of $t=2m/j$. So, for the second variant of the experiment there exists two the largest closely related peaks at ${j}_{1}^{\left(2\right)}$ = 3 and ${j}_{2}^{\left(2\right)}$= 4. Consequently, the frequency of transpiration is equal to ${t}_{1}^{\left(2\right)}\approx 19$ and ${t}_{2}^{\left(2\right)}=14$ days (and nights) for the maxima intensity of the harmonics of the second variant. These vibrations are the low-frequency or the long-period oscillations. There are also other harmonical oscillations (Figure 4) with the periodicities are equal to ${t}_{3}^{\left(2\right)}=4.7$ (j = 12) and ${t}_{4}^{\left(2\right)}=2.7$ (j = 21) days (and nights), but they are much lower on the intensity of the first two periodicities. A similar situation occurs for the fourth variant of the experiment. There are two very intense close peaks: ${j}_{1}^{\left(4\right)}$ = 2 and ${j}_{2}^{\left(4\right)}$ = 5 which correspond to the following periodicities: ${t}_{1}^{\left(4\right)}=28$ and ${t}_{2}^{\left(4\right)}=11.2$ days (and nights). The existence of low-frequency peaks (small values of j) for the harmonic oscillations of the second and the fourth variants are not a manifestation of the random nature of the time series 17. So, for the variants 1 and 3 also there are small power peaks in the range of j = 2 - 5, however, these maxima, in particular for the variant 1, considerably are inferior to other maximums high intensity (Figure 4).

Considerable interest has the third variant of the experiment for which we obtained the maximum plant productivity. This variant is characterized by two the most peaks of equal power in the spectrum, moreover these maxima significantly spaced apart ${j}_{1}^{\left(3\right)}$ = 3 and ${j}_{2}^{\left(3\right)}$ = 20. Features of this analogue of soil consist in that we found two equal the maxima with the most intensity in spectrum. Moreover, these maxima correspond to the low-frequency periodicity (${t}_{1}^{\left(3\right)}=18.7$ day (and night)) and the high-frequency periodicity of the transpiration process (${t}_{2}^{\left(3\right)}=2.8$ day (and night)). Thus, the third variant is differed from all other variants the presence of two oscillating processes that have equal power, i.e., long-wave and short-wave vibrations. From Figure 4, we can see that the frequency spectrum of the fourth variant is qualitatively similar to the frequency spectrums of the second and the third variants. The result does not contradict to the conclusion we have obtained by the method of associations of qualitative features (Table 1).

Figure 4.
The intensity of the spectrum Uj. - ♦ - ♦- variant 1, - ■ - ■ - variant 2, •▲• ▲• variant 3, -× - variant 4.

Increase of a range of the frequency bands m for the spectrum there is no sense, since it would lead to the appearance of short-wave or high-frequency periodicities, for which the value of time ${t}_{}^{\left(i\right)}$< 1 day (and night). The periodicities are doubtful with periods of less than one unit of time (in this case, one day (and night)) 18. If we use a time interval equal to one day (and night) then we can not consider oscillations as reliable with a period of less than two days or higher frequency of $\pi /\Delta t$ (the limiting frequency of Nyquist; $\Delta t$ = 1 day (and night) is the time interval between adjacent observations).

The first variant is clearly distinguished of the other variants. For this variant, there is a major peak in the spectrum of the intensity of the frequency domain (${j}_{1}^{\left(1\right)}$$\approx$ 8; ${t}_{1}^{\left(1\right)}=7$ day (and night)), where for the other variants detected intensity minimum. For the first variant, there is the intensity maximum of the spectrum at ${j}_{3}^{\left(1\right)}$= 3 (${t}_{3}^{\left(1\right)}\approx 19$ days (and nights)), precisely in the area, where for the other variants exist the minimum of the power periodicity. Similar contrasting situation is observed for the high-frequency periodicity in the area of j = 20-22. In addition, we must note that in the first variant there are six of harmonic components of the different power, while the second and third variants there are only four periodicities. Thus, spectral analysis confirms the clear-cut distinction of variant 1 from other variants and these results do not contradict to the results of the qualitative analysis presented in Table 1. Obviously, the distinctions in the periodicities of water exchange of tomato plants caused by the peculiarities of soil analogues. Knowledge of the structure of the oscillatory process allows us to find the link between the periodicity of plant transpiration and the productivity of phytocenoses under controlled conditions.Analysis of tomato plants productivity showed that plants of the third variant had the highest productivity (976 ± 61 g/plant). The fourth variant showed the lowest productivity (540 ± 56 g / plant). For the variants 1 and 2 the productivity of plants is equal to 758 ± 59 and 708 ± 64 g/plant respectively. In addition it should be noted that to the advantages of the third variant we must denote very early (~ 21 day (and night)) reaching of the trend maximum of the water consumption by plants. To reach the maximum of the trend for other variants of the experiment it takes time from 27 to 35 days (and nights). Analysis of plant productivity showed that TJAS onto surface of the mulch and the substrates for growing seedlings creates the most favorable conditions for the development and functioning of the root system of the plants. This is probably due to the fact that composition of soil analogues includes the fine-dispersed organo-mineral components. These components are enriched with macro-and microelements, as well as biologically active substances.Apparently, the variant 3 is characterized by the optimal conditions of life support for plant root systems.

Studies of the absorption dynamics of chemical elements in the tomato plants showed their oscillatory nature for all variants of the experiment (Figure 5, Figure 6, Figure 7, Figure 8, Figure 9). Spectral analysis of the time series revealed the presence of the essential harmonic component in structure of the absorption of chemical elements For calcium and phosphorus most powerful harmonic component has the period 2 weeks (14 days (and nights)) for most variants. Only for the fourth variant of calcium and phosphorus for the third variant the length of a period increases up to 4 weeks (28 days (and nights)), and the oscillation frequency decreases.

Figure 5.
Dynamics of calcium content (mmol/plant) in tomato plants. - ♦ - ♦- variant 1, - ■ - ■ - variant 2, •▲• ▲•variant 3, - • -× - • -× variant 4.
Figure 6.
Dynamics of phosphorus content (mmol/plant) in tomato plants - ♦ - ♦- variant 1, - ■ - ■ - variant 2, •▲• ▲•variant 3, - • -× - • -× variant 4.

Effect of TJAS composition is not very essentially for the most intense periodical frequency of absorption processes of potassium, magnesium and nitrate nitrogen. The dominating periodicity is characterized by a low frequency oscillation equal to four weeks for all variants of the experiment. Comparing periods of oscillation of the chemical elements absorption in plants with the most intense periodicities of the water exchange, we can note the close relationship between them. Indeed, the greatest intensity of oscillation of the transpiration is located in a time interval of 14-28 days and nights (j = 2-4; Figure 7) for variants of 2, 3 and 4. We should be note that for the variant 1 also has a maximum periodicity of the transpiration in the same field j = 3, but as mentioned above, this the maximum of periodicity power below of main maximum.

Figure 7.
Dynamics of nitrates (mmol/plant) in tomato plants. - ♦ - ♦- variant 1, - ■ - ■ - variant 2, •▲• ▲•variant 3, - • -× - • -× variant 4.
Figure 8.
Dynamics of potassium content (mmol/plant) intomatoplants. - ♦ - ♦- variant 1, - ■ - ■ - variant 2, •▲• ▲•variant 3, - • -× - • -× variant 4.
Figure 9.
Dynamics of magnesium content (mmol/plant) intomato plants. - - - variant 1, - - - variant 2, variant 3, - -× - variant 4.

Noticeably the influence of the composition TJAS on trend component that determines the general direction of the long-term evolution of chemical elements absorption processes by plants. So, for the third variant the content of calcium, nitrate nitrogen and phosphorus indicates the dynamics (trend) of reducing their absorption by plants during the vegetation. At the same time, the use of other compositions TJAS leads to inverse trend, that is, to increase the absorption of these elements by the end of the growing season. We found a significant absorption of nitrate nitrogen in the plants for variant 4, where there was no covering of the spunbond by TJAS, and seedlings were grown on the hydrophilic microporous plastic.

For all variants of the experiment the trend of magnesium shows that there is a reduction of magnesium absorption by the end of the growing season.The third variant is characterized by the minimum rate of descent of magnesium absorption. For the fourth variant we found maximum speed of reduction of magnesium absorption. Trends show the rise of the phosphorus absorption for all variants of the experiment by the end of the growing season. Trends for calcium, potassium and nitric nitrogen correlated. For the first and second variants there exists the trend of increase of the absorption of these elements in plants with the age of the plants. At the same time for the third and fourth options there exists cooperative decrease of their absorption. Composition of TJAS only affects the rate of the deterministic processes. As shown by the statistical analysis, the processes of absorption of nitrate nitrogen are carried out much more rapidly than for absorption of calcium and potassium. The authors 14 also indicate some commonality of the absorption dynamics by the tomato plants of Са2+, К+ and NO${}_{3}^{-}$.

Experimental data have shown that the greatest quantitative distinction in the absorption of chemical elements is observed for variant 4. In this case sprouts were grown on microporous plastic, and mulch was not coated by TJAS. Indeed, we have found that the chronological average values for the absorption of potassium, magnesium, phosphorus and nitrate nitrogen are the largest for the variant 4. Mean calcium absorbtion in the variant 4 also sufficiently high, and only slightly inferior to the third variant. However, such the trend behavior of chemical elements absorption are not promoted increasing the productivity of plants for this variant. Here we should note that in the fourth variant missing the fine-dispersed organic and mineral components. These components facilitate the creation a more favorable the trophic environment, which affects the dynamics of plant transpiration and absorption dynamics of chemical elements by plants. Apparently, it has affected significantly the reduction of a plant productivity.

### 4. Conclusion

The studies showed that the use TJAS as new, thin-layer, ecologically clean, single-use rooting medium may be promising solution of the problem to maintain high productivity of plants under controlled conditions. TJAS provides for the conditions that close to the optimal living conditions for roots. TJAS not gives rise to perturbations in RIS that could affect the normal processes of nutrition of plant roots. For example, the intensive cultivation of plants on mineral RIS is accompanied by the transformation of their properties. This leads to a processes that analogous to the primary soil formation in natural conditions 1.

Application of TJAS for coating on synthetic, mineral and organic RIS can be regarded as the methodological basis for the optimization of the conditions of life support plant root system. Spectral analysis of the results of experiments on the transpiration of tomato plants showed that the main trend of the process of transpiration has a parabolic dependence and curve shape does not depend on the composition of TJAS. Changing of the composition of TJAS only shifts the maximum of the trend in the timeline and changes a value of the maximum.

Method of the spectral analysis of the one-dimensional time series allowed us to detect a structural difference in the periodicities of the processes of water-mineral metabolism in tomato plants for different of TJAS compositions. For example, the third variant, which gives the highest productivity of tomato plants, is characterized by two largest values of equal intensity periodicities, i.e., the periodicity of high-frequency (period ${t}_{2}^{\left(3\right)}=2.8$ days (and nights); oscillation frequency is equal to ${\omega }_{1}^{\left(3\right)}=0.714×\pi$, (days (and nights))-1) and the periodicity of low-frequency (period ${t}_{1}^{\left(3\right)}=18.7$ days (and nights); oscillation frequency, ${\omega }_{1}^{\left(3\right)}=0.107×\pi$, (days (and nights))-1. For the second and the fourth variants there exist also two periodicities with largest values of the intensities. However, them are the periodicities of low-frequency, with very close frequencies of oscillations. For these variants of TJAS it is characteristic smallest plant productivity. For the variant 1 in the mechanism of plant transpiration there exist only one maximum of the periodicity in the frequency range, which is missing in the other variants. The plant productivity in this variant is lower markedly of the productivity for the third variant. We also are noted that there exists a weak correlation between the productivity of tomato plants with the reciprocal of the maximum intensity of the principal periodicity of the plant transpiration.

Apparently, most favorable situation to maximize plant productivity, when the composition of TJAS creates the following conditions. Firstly, the mechanism of water use plants must be present at the same time the long-wave and short-wave frequency equal and maximum power. Secondly, the transpiration of plants should reach of the trend maximum for a very short time.

The experiment showed the prospectivity to use of TJAS for growing plants under controlled conditions. Using disposable of TJAS opens the possibility to implement hold of the RIS in the juvenile highly active state. This method may be promising for practical purposes the obtaining of ecologically clean plant products, modeling of effective soil analogues and to develop new ways to control plant productivity by optimizing the conditions of life support plant root system. Findings the comprehensive experimental material can be used as an information base for model studies in plant physiology, including water and mineral metabolism in almost perfect conditions of CAES.

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