Theory of small-scale self-focusing of spatially partially coherent beams and its implications for high-power laser systems

Based on the paraxial wave equation,this study extends the theory of small-scale self-focusing(SSSF)from coherent beams to spatially partially coherent beams(PCBs)and derives a general theoretical equation that reveals the underlying physics of the reduction in the B-integral of spatially PCBs.From the analysis of the simulations,the formula for the modulational instability(MI)gain coefficient of the SSSF of spatially PCBs is obtained by introducing a decrease factor into the formula of the MI gain coefficient of the SSSF of coherent beams.This decrease can be equated to a drop in the injected light intensity or an increase in the critical power.According to this formula,the reference value of the spatial coherence of spatially PCBs is given,offering guidance to overcome the output power limitation of the high-power laser driver due to SSSF.

Small-scale self-focusing of divergent beam in nonlinear media with loss

Bespalov-Talanov theory on small-scale self-focusing is extended to include medium loss for a divergent beam. Gain spectrum of small-scale perturbation is presented in integral form, and based on the derived equations we find that the cutoff spatial frequency for perturbation keeps a constant value. The larger the medium loss is, the smaller the fastest growing frequency and the maximum gain of perturbation with defined propagation distance are. For a given medium loss the maximum gain of perturbation becomes larger, while the fastest growing frequency becomes smaller as the propagation distance becomes longer. Furthermore, physical explanations for the appearance of these features are given.

Analysis and Innovative Strategies of Tax Preferential Policies to Promote the Sustainable Development of Small-Scale Individual Businesses

This study conducted an in-depth analysis of the current tax preferential policies for small-scale individual businesses and compared them with similar policies both domestically and internationally,aiming to reveal the advantages and disadvantages of the current system.After examining the impact of these tax preferential policies on the economic status of individual business owners and the broader social economy,this article proposes a set of innovative tax preferential strategies based on theoretical foundations.By developing these innovative strategies and clarifying their implementation paths,the aim is to promote the sustainable and healthy development of small-scale individual businesses,thereby fostering comprehensive socio-economic progress.The conclusion of this study not only summarizes policy recommendations with practical significance but also provides theoretical support for the optimization and innovation of future related systems.

Model of small-scale self-focusing and spatial noise in high power laser driver

A linearization model was used to analyze the laser beam propagation in a high power laser driver and the influence of the small-scale self-focusing and spatial phase noise on beam quality in disk amplifiers. The quantitative relations between intensities of spatial phase noise, B-integral, and beam intensity contrast in near field are given explicitly. A spectrum specification of phase noise has been obtained by setting a limit to the contrast of an output beam.

Experimental research of pulsed chirp effect on the small-scale self-focusing

The chirped optical pulses undergoing self-focusing and splitting into multiple filamentation passing through a Kerr medium-carbon disulfide (CS2) are studied experimentally and numerically. At the particular spatial position, modulation growth takes place from the experimental result. The process of modulation growth with different pulsed chirp is analyzed. It is found that with the pulsed chirp in-creasing (equal to the pulse width increasing), modulation growth of chirped opti-cal pulses is delayed and the average input power also increases. The simulation results are in agreement with the experimental results.

An analytical model for estimating rock strength parameters from small-scale drilling data

The small-scale drilling technique can be a fast and reliable method to estimate rock strength parameters. It needs to link the operational drilling parameters and strength properties of rock. The parameters such as bit geometry, bit movement, contact frictions and crushed zone affect the estimated parameters.An analytical model considering operational drilling data and effective parameters can be used for these purposes. In this research, an analytical model was developed based on limit equilibrium of forces in a Tshaped drag bit considering the effective parameters such as bit geometry, crushed zone and contact frictions in drilling process. Based on the model, a method was used to estimate rock strength parameters such as cohesion, internal friction angle and uniaxial compressive strength of different rock types from operational drilling data. Some drilling tests were conducted by a portable and powerful drilling machine which was developed for this work. The obtained results for strength properties of different rock types from the drilling experiments based on the proposed model are in good agreement with the results of standard tests. Experimental results show that the contact friction between the cutting face and rock is close to that between bit end wearing face and rock due to the same bit material. In this case,the strength parameters, especially internal friction angle and cohesion, are estimated only by using a blunt bit drilling data and the bit bluntness does not affect the estimated results.

Numerical Simulation for Accuracy of Velocity Analysis in Small-Scale High-Resolution Marine Multichannel Seismic Technology

When used with large energy sparkers, marine multichannel small-scale high-resolution seismic detection technology has a high resolution, high-detection precision, a wide applicable range, and is very flexible. Positive results have been achieved in submarine geological research, particularly in the investigation of marine gas hydrates. However, the amount of traveltime difference information is reduced for the velocity analysis under conditions of a shorter spread length, thus leading to poorer focusing of the velocity spectrum energy group and a lower accuracy of the velocity analysis. It is thus currently debatable whether the velocity analysis accuracy of short-arrangement multichannel seismic detection technology is able to meet the requirements of practical application in natural gas hydrate exploration. Therefore, in this study the bottom boundary of gas hydrates(Bottom Simulating Reflector, BSR) is used to conduct numerical simulation to discuss the accuracy of the velocity analysis related to such technology. Results show that a higher dominant frequency and smaller sampling interval are not only able to improve the seismic resolution, but they also compensate for the defects of the short-arrangement, thereby improving the accuracy of the velocity analysis. In conclusion, the accuracy of the velocity analysis in this small-scale, high-resolution, multi-channel seismic detection technology meets the requirements of natural gas hydrate exploration.

Weak wide-band signal detection method based on small-scale periodic state of Duffing oscillator

The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator＇s phase trajectory in a small- scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system.

Factors affecting technical efficiency of small-scale apple farms in Balochistan Plateau, Pakistan

In Balochistan, Agriculture is dominated by small-scale farmers and the apple production sector is confronted with the chronic constraint of low output per unit of input. Although some agricultural policies have been implemented in this province, studies on effectiveness and impacts of such policies over apple production and farmers' performance are still limited. This study is an effort to bridge the research gap on this potential crop in the plateau by investigating technical and scale efficiency of 181 officially designated small-scale apple farmers in mountainous district Mastung in Balochistan; then explored factors that underlie differences in production inefficiency. A two-stage input-oriented Data Envelopment Analysis(DEA) methodology was employed to evaluate technical and scale efficiency followed by truncated bootstrapped regression framework to analyze the correlative determinants to efficiency. Average technical and scale efficiencies of larger landholders were higher than medium and small landholders. Analysis indicated that there is still ample scope for inefficient sample farmers to reduce the input use by 33% without compromising the given yield level. Maximum contributions to the total input savings were from the use of urea, farm yard manure(FYM) and labor-use. Farmer's experience, farm ownership, irrigation constraints, and farmer's access to trainings, credit and extension services significantly affected apple farmers' technical efficiency. Based on the findings of this study, strategies are suggested to enhancing efficiencies by farmers' capacity development through effective extension services and trainings and provision of adequate credit.

Shock-induced fracture of dolomite rock in small-scale blast tests

This paper attempts to study dolomite failure using small-scale blast tests.The experimental setup consisted of a cylindrical specimen with a central borehole fitted with a detonation cord inside a copper pipe.The specimen was confined using lead material.During the test,acceleration histories were recorded using sensors placed on the lead confinement.The results showed that heterogeneity and initial cracks significantly influenced the observed failure and cracking patterns.The tests were numerically represented using the previously validated Johnson-HolmquistⅡ(JH-2)constitutive model.The properties of the detonation cord were first determined and verified in a special test with a lead specimen to compare the deformation in the test with that of numerical simulation.Then,the small-scale blast test was simulated,and the failure of the dolomite was compared with the test observations.Comparisons of acceleration histories,scabbing failure,and number of radial cracks and crack density confirmed the overall repeatability of the actual testing data.It is likely that the proposed model can be further used for numerical studies of blasting of dolomite rock.

Study on the Roles of FWUA in Construction, Management and Maintenance of Small-Scale Irrigation and Water Conservancy

In recent years, China has been frequented by floods and droughts which has greatly evoked much concern from the Central Government about rural water conservancy construction. Irrigation is closely related to the "three rural" issues and concerns about the vital interests of farmers. To achieve a virtuous circle of agricultural water supply, it is necessary and urgent to establish Farmer Water User Association (FWUA) to participate in the construction, management and maintenance of small-scale irrigation system. Based on the survey on nationwide "Small-scale irrigation conditions", the roles of FWUA in the construction, management and maintenance of small-scale water conservancy have studied in this study.

Effect of high-or low-speed fluctuations on the small-scale bursting events in an active control experiment

Active control of a fully developed turbulence boundary layer(TBL) over a flat plate has been investigated with a statistical view. The piezoelectric(PZT) oscillator is employed to produce periodic input into the inner region of the TBL.A wall probe is fixed upstream of the oscillator to identify the high-or low-speed fluctuations as the detecting signals.Then, the impact of the detecting signals on the small-scale bursting process is investigated based on the data acquired by the traversing probe downstream of the oscillator. The results indicate that the small-scale bursting intensity is restrained more apparently at high-speed detecting fluctuations but less impacted at low-speed detecting fluctuations. Furthermore, the perturbed-scale fluctuations arrange the small-scale bursting process in the near-wall region. The detecting signals have an obvious impact on this arrangement, especially the high-intensity regions of the small-scale bursting events: the vibration enhances the intensity at high-speed detecting signals but weakens it at low-speed detecting signals in these regions, which gives a direct evidence on how detecting signals interfering the small-scale bursting process.

Small-Scale Tomato Cultivators’ Perception on Pesticides Usage and Practices in Buea Cameroon

It has been shown that farmers with limited knowledge of the use and safe handling of pesticides may suffer exposure which results in adverse health effects. In Buea, Cameroon, small-scale tomato farmers commonly use pesticides for pest control. Information was obtained from these tomato farmers to determine the extent and types of their pesticide use, their knowledge of pesticide use and effectiveness, and their perception of potential harm resulting from pesticide use. A standardized questionnaire, interviews, field observations and an analytical ranking game were used to describe the pesticide use of 93 tomato farmers. Many farmers (47.6%) used pyrethiod and organophosphorus insecticides and identified these chemicals as the most effective in pesticide control;these are WHO Class II pesticides which are the most hazardous to humans. Most farmers (83.8%) used knapsack sprayers to apply pesticides, with 76.3% using no or partial personal protective equipment (PPE). It was notable that 55.5% of farmers expressed no concern regarding the wind direction (pesticide drift) during spraying. The results showed a significant association between the method of pesticides application and farm size (P < 0.001). Most farmers (85.0%) reported at least one symptom of acute pesticide poisoning following spraying. This study revealed that the tomato farmers have a high exposure to pesticides secondary to inadequate knowledge of the safe and judicious use of pesticides. Strategies that provide training on the appropriate use of pesticides, how to reduce exposure to and health risks of pesticides and alternative options of pest management and control are required. The study also raised concerns that further control of the sale and distribution of pesticides may be indicated.

Processes of small-scale tidal flat accretion and salt marsh changes on the plain coast of Jiangsu Province,China

Large-scaled reclamation modifies the coastal environment dramatically while accelerating the disappearance of salt marshes,which causes the degradation of the coastal ecosystem and the biodiversity function.In this study,we explored the changes of tidal flat and salt marsh coverage in a small-scale tidal flat with an area of ~160 000 m^2 in the plain coast of Jiangsu Province,China.Human activities（e.g.,the construction of dikes） are a crucial contributor that benefits for the tidal flat accretions and the following changes of salt marsh coverage.Located in the front of the man-made ＂concave coastline＂,the study area is suitable for sediment accretion after the dike construction in the end of 2006.On the basis of the annual tidal surface elevation survey from 2007 to 2012,the sedimentation rates in the human influenced tidal flat varied from a few centimeters per year to 23 cm/a.The study area experienced a rapid accretion in the tidal flat and the expansion of the salt marsh,with the formation of a longshore bar,and a subsequent decline of the salt marsh.Breaking waves during the flooding tide brought much sediment from the adjacent tidal flat to the study area,which caused burial and degeneration of the salt marsh.The vertical grain size changes within a 66 cm long core in the study area also demonstrated the above changes in the tidal environment.This study indicates that the responses of small-scale tidal flat changes to reclamation are significant,and the rational reclamation would benefit for the new salt marsh formation in front of the dikes.Further research about the evolution of small scale tidal flat as well as the spatial planning of the polder dike should be strengthened for the purpose to maintain a healthier coastal environment.

Self-compression of femtosecond pulses in argon with a power close to the self-focusing threshold

Self-compression of femtosecond pulses in noble gases with an input power close to the self-focusing threshold has been investigated experimentally and theoretically. It is demonstrated that either multiphoton ionization （MPI） or space-time focusing and self-steepening effects can induce pulse shortening, but they predominate at different beam intensities during the propagation. The latter effects play a key role in the final pulse self-compression. By choosing an appropriate focusing parameter, action distance of the space-time focusing and self-steepening effects can be lengthened, which can promote a shock pulse structure with a duration as short as two optical cycles. It is also found that, for our calculation cases in which an input pulse power is close to the self-focusing threshold, either group velocity dispersion （GVD） or multiphoton absorption （MPA） has a negligible influence on pulse characteristics in the propagation process.

Characteristics of Self-Focusing Dueto the Pondermotive Forcein Laser-Plasma Interaction

The Max’s equation of self-focusing in laser-plasma interaction due to the pondermotive force has been discussed and its physical meaning of the assumption has been predicted. The characteristics of selffocusing due to the pondermotive force with different initial situations have been analyzed through the numerical calculation.

The Human Dimension in the UNESCO Kogelberg Biosphere Reserve:Integrating Livelihood Issues of Small-Scale Fisheries with the Conservation of Natural Resources

Fisheries management worldwide struggles to strike a balance between protecting resources,ensuring fair access to resources and promoting economic effectiveness and stability.The transition to a participatory democracy in South Africa in 1994 resulted in the transformation of government institutions and an extensive process of legislative reform regarding

Small-Scale Duplications Play a Significant Role in Rice Genome Evolution

Genes are continually being created by the processes of genome duplication （ohnolog） and gene duplication （paralog）. Whole-genome duplications have been found to be widespread in plant species and play an important role in plant evolution. Clearly un-overlapping duplicated blocks of whole-genome duplications can be detected in the genome of sequenced rice （Oryza sativa）. Syntenic ohnolog pairs （ohnologues） of the whole-genome duplications in rice were identified based on their syntenic duplicate lines. The paralogs of ohnologues were further scanned using multi-round reciprocal BLAST best-hit searching （E〈e^-14）. The results indicated that an average of 0.55 sister paralogs could be found for every ohnologue in rice. These results suggest that small-scale duplications, as well as whole-genome duplications, play a significant role in the two duplicated rice genomes.

Transverse Localization of Light in 1D Self-Focusing Parity-Time-Symmetric Optical Lattices

Transverse localization of light is investigated numerically in a serf-focusing Kerr medium with a complex-valued optical lattice featuring parity-time symmetry. It is demonstrated that the light localization exists below the threshold of the spatial frequency of the lattices, and is further enhanced with the decrease of the spatial frequency. The influence of defects on the transverse localization is also discussed in detail. The results show that both positive and negative defects in such a medium would enhance the localization.

Density disturbance of small-scale fieldaligned irregularities in the ionosphere heating experiments

A theoretical model which describes the small-scale irregularities excited by powerful high frequency （3–30 MHz） electromagnetic wave in ionosphere heating is investigated quantitatively in this paper. The model is based on the transport equation in magnetic plasma and mode conversion from electromagnetic wave to electrostatic wave in ionospheric modification.Threshold electric field for exciting small-scale （meter scale） irregularities and spatial spectra of irregularities are analytically calculated by this model. The results indicate that background electron density and geomagnetic field play an important role for the threshold electric field and the spatial scale of the electron density irregularities. The results demonstrate that the electric field threshold increases with the decrease of the spatial scale of the irregularities. For exciting meter scale irregularities, the threshold electric field is about tens of mV m^（-1）. The theoretical results are consistent with those of the experiments.