Mechanical Character Research Articles

Design and performance of a novel multi-leaf collimator composed of leaves with fixed and movable layers.

The multi-leaf collimator (MLC) is an advanced device utilized for beam shaping and intensity modulation in radiotherapy. With the framework of the contemporary single-layer MLC featuring a rounded leaf tip, the leaf tip transmission and leakage exert a considerable influence on radiotherapy. To scale down the leakage and transmission from the leaf gap when the opposite leaves are closed. This study proposes a new design of MLC, named dynamic leaf machine (DLM), specifically engineered to diminish the transmission and leakage from the MLC leaf tip. The DLM incorporates an innovative leaf configuration that involves a combination of fixed and movable layers in a single MLC leaf named fixed and movable (FM) layers leaf, which is advantageous in dealing with transmission and leakage from the leaf tip by employing a staggered arrangement of the fixed and movable layer when the opposite leaves are closed. Subsequently, the DLM is assembled on the Elekta VERSA HD accelerator to assess its performance, focusing on aspects of mechanical characters, transmission, leakage, and penumbra. In comparison to conventional MLC leaves, the FM leaf design in the DLM has achieved a remarkable reduction in the leakage between opposed closed leaves, decreasing it from 48.41% to 0.41%. Additionally, the transmission between the adjacent leaves has been measured at 0.59%, and the penumbra in 16mm × 32mm field is 2.82mm, aligning with the performance of conventional MLC. The DLM with FM leaf performs a significant reduction in transmission from the opposite leaf tip in comparison to conventional MLC while maintaining minimal penumbra, effectively mitigating the transmission and leakage problem between opposing leaves, thereby enhancing the effect of radiotherapy.

Feasibility Evaluation of I–Shaped Horizontal Salt Cavern for Underground Natural Gas Storage

Underground salt cavern gas storage has been widely applied due to its numerous advantages. Most of China’s salt resources are derived from lacustrine deposits. As high–quality resources in the central sedimentary area are gradually exploited, exploring the utilization of thin salt layers at the edges of sedimentary centers is the future development trend. However, the use of thin salt layers faces challenges such as low resource utilization, small cavern volumes, and poor economic feasibility, which limit its engineering applications. Therefore, a comprehensive assessment of constructing gas storage in thin salt layers is necessary. This paper first analyzes the necessity of building gas storage in thin salt layers and surveys cavern construction methods and their applicability. Based on geological seismic data, the feasibility of constructing gas storage in the Pingdingshan thin salt layer is proposed. A novel I–shaped cavern design is introduced, which, according to engineering economic evaluations, reduces investment by 9.6% compared to traditional single–well vertical cavern construction methods. Finally, rock mechanics tests were conducted to study the impact of mudstone interlayers and cyclic operation modes on the stability of the I–shaped cavern under three different injection and production conditions. The analysis shows that multi–cycle injection and production can effectively suppress cavern shrinkage and the development of the rock–relative plastic zone. The safety factor (SF) for different conditions is greater than 1, indicating that the I–shaped cavern has good stability and can adapt to various operational conditions. This study provides valuable insights into the geological conditions and rock mechanics characteristics for the future construction of gas storage in thin salt layers in China.

Structure, Optical and Electrical Properties of Nb(Zn) Doped Sol-Gel ITO Films: Effect of Substrates and Dopants.

We present comparative studies of sol-gel ITO multilayered films undoped and doped with Nb or Zn (4 at.%). The films were obtained by successive depositions of five layers using the dip-coating sol-gel method on microscopic glass, SiO2/glass, and Si substrates. The influence of the type of substrates and dopant atoms on the structure and optical properties of the sol-gel ITO thin films is examined and discussed in detail. XRD patterns of these layers showed a polycrystalline structure with an average crystallite size of <11 nm. Raman spectroscopy confirmed the chemical bonding of dopants with oxygen and showed the absence of crystallized Nb(Zn)-oxide particles, indicated by the XRD pattern. Spectroscopic Ellipsometry and AFM imaging revealed a clear dependence of the optical parameters and surface morphology of the ITO and ITO:Nb(Zn) thin films on the type of substrates and dopants. The analysis of the current-voltage and capacitance-voltage characteristics of the Al/ITO/Si structures revealed the presence of charge carrier traps in the ITO bulk and the ITO-Si interface. The densities of these traps are obtained and the character of the current transport mechanism is established.

Mechanical Characters of Geo-Polymer Concrete for Major Alteration of Cement by Fly Ash

Fly Ash (FA) production exceeded 250 million tons in India by the year 2020 and it would exceeds 450 million tons by the year 2025. This creates huge problems for storage of waste. And it requires hectors of lands to store. It is classified in Class – C and Class – F. Class – C has Pozzolanic properties and self-Cementitious rather to Class – F which attains the same properties by addition of activator. Alkali and Sulfate content in Class – C are higher. Use of Major volume fly ash in addition to lime and admixtures may be permitted to act as Pozzolanic Binder in ordinary concrete to form Geo-Polymer Concrete (GPC). Basically GPC, a Green Concrete (Eco-Friendly Concrete) also made in another way by adding FA, Rice Husk Ash (RHA), Steel Furnace Slag (SFS) and Alkali Activators (AA) following the same process as that of OPC. As the previous studies focuses on strength evaluation of Class – C. The prime objective of this study to examine the comparative characteristics of major alteration of Class – F with Low Calcium GPC subjected to the Tropical Environment with OPC. The findings are observed in the term of Consistencies and it varies from 31 % to 45 % for 0 % alteration of cement to 80 % and lowering and undefined value for 90 % alteration and 100 %. The consistency findings are also observed in progressive range of 32 % to 39 % for addition of Dry Lime from 0 % to 4.5 % (Table - 8) and undefined for 5 % addition. Later on it is observed for 10 % and 15 % addition which shows progressive results. Compression Character (Table - 10) and Flexural Character (Table - 11) is determined for various percentage alteration of PFA and it shows progressive results up to 80 % alteration and percentage difference of 69 % to 85 % for 90 % alteration.

Novel adsorbent based on Argan Spinosa leaves modified with citric acid for effective removal of crystal violet dye from textile effluents

Over the recent decades, water contamination has surged, emerging as a critical global concern. This study focuses on the removal of crystal violet (CV) dye from water, employing citric acid-modified Argan Spinosa leaves (CA@Arg-Sp) as effective adsorbent. The newly functionalized adsorbent were examined using SEM, FTIR and TGA/DTA. In addition, thermal stability tests demonstrated that the CA@Arg-Sp material maintains structural integrity up to 260 °C. The study tested the efficacy of CA@Arg-Sp in removing CV dye from wastewater up to 99.5 % at pH 7. Electrostatic attractions and hydrogen bonding were identified as crucial factors enhancing CV adsorption. Adsorption performance was further analyzed concerning adsorbent dosage, initial dye concentration, temperature, contact time, and pH. Freundlich isotherm and pseudo-second-order models provided excellent fits for both isotherm and kinetic adsorption simulations. CA@Arg-Sp demonstrated a maximum adsorption capacity of 335.09 mg g−1. Thermodynamic investigations confirmed the endothermic and spontaneous character of the CV elimination mechanism. In general, CA@Arg-Sp is a low-cost, regenerative, and eco-friendly adsorbent for textiles effluents treatment.

Rock failure deformation characteristics and mechanical parameter prediction of Xujiahe formation gas reservoir in Tianfu area, Sichuan Basin

The integrated geological-engineering reservoir reconstruction of Xujiahe Formation in Tianfu area needs accurate evaluation of rock mechanics characteristics and prediction of three-dimensional rock mechanics parameter field. The stress-strain curve characteristics, failure deformation mode, mechanical strength, and confining pressure effect are analyzed by mechanical tests. The longitudinal, lateral, and spatial distribution characteristics of rock mechanics parameters are evaluated through the combination of logging and seismic. The results show that damage morphology of mudstone is more complex than that of sandstone. With the increase of confining pressure, rock fracture pattern gradually changes from splitting failure to high angle shear failure. The mechanical strength of sandstone and mudstone increases with the increase of confining pressure, and high porosity of sandstone results in a higher confining pressure effect. The longitudinal distribution of rock mechanics parameters is significantly affected by lithology. Sandstone has high strength and little intra-layer difference, while mudstone is the opposite. The lateral distribution shows obvious sedimentary facies control characteristics, and the mechanical strength of rock in the northwest region is significantly lower than that in the southeast region. The spatial distribution is greatly affected by structural morphology and faults. The research will provide support for engineering dessert selection and fracturing reconstruction.

Mechanical behaviour and instability mechanism of sandstones with impact tendency under different loading paths

ABSTRACT To reveal the instability and failure mechanism of pillars with impact tendency, the Brazilian test, uniaxial compressive test, cyclic loading and unloading (CLU) tests were performed on sandstones which had impact tendency. The stress drop phenomenon was obvious in the fracture stage during the Brazilian test. The main tensile crack with penetration type appeared. Under the CLU condition, the CLU had a significant effect in enhancing the mechanical character of rocks. Under the combined loading, the character stress of rocks tested with the CLU was greater than the uniaxial loading. Moreover, the greater the first cyclic threshold, the greater the character stress of rocks. Under the uniaxial loading, the failed samples showed tensile fractures. The damage location of the samples was closely related to the Poisson effect and the ending face effect. With the electron microscope which had the same magnification, the crack deterioration degree of samples under the uniaxial loading was greater than the CLU condition. Moreover, with the first cycle threshold increasing, the surface roughness of rocks gradually decreased. The quantity of secondary micro cracks gradually decreased. The propagation and penetration phenomenon gradually disappeared. The micro structure and loading properties of rocks were affected by the bonding force and structural characters between the internal structure and matrix. Based on the micro-seismic signal of the damaging threshold, the seismic source damage location can be located. Moreover, the pillar-typed burst area can be forewarned. This research benefits predicting the pillar-typed burst disaster.

Theoretical insights into a turn-on fluorescence probe based on naphthalimide for peroxynitrite detection

Compared with other reactive oxygen species, peroxynitrite (ONOO−) has diversified reactions and transformations in organisms, and its specific action mechanism is not very clear. The study of reactive oxygen species is of great significance in the field of physiology and pathology. Recently an effective on/off fluorescent probe HCA-OH was designed by Liu et al. through tethering p-aminophenol to 1,8-naphthalimide directly. The probe HCA-OH could release the fluorophore HCA-NH2 with good photostability and high fluorescence quantum yield under oxidation of ONOO− via dearylation process. In this work, the sensing mechanism and spectrum character of probe HCA-OH were studied in detail under quantum chemistry calculation. The electronic structures, reaction sites and fluorescent properties of the probe were theoretically analyzed to benefit us for in-depth understanding the principle of detection on reactive oxygen species (ONOO−) with the fluorescent probe HCA-OH. These theoretical results could inspire the medical research community to design and synthesize highly efficient fluorescent probe for reactive oxygen species detection.

The mechanical, thermodynamic and electronic characters of TiFe at extreme pressures: first-principles calculation

The mechanical, thermodynamic and electronic characters of TiFe at extreme pressures: first-principles calculation

Research into mechanical modeling based on characteristics of the fracture mechanics of ice cutting for scientific drilling in polar regions

Abstract. Scientific drilling in polar regions plays a crucial role in obtaining ice cores and using them to understand climate change and to study the dynamics of polar ice sheets and their impact on global environmental changes (sea level, ocean current cycle, atmospheric circulation, etc.). Mechanical rotary cutting is a widely used drilling method that drives the cutter to rotate to cut and drill through ice layers. It is necessary to conduct in-depth research on the brittle fracture behavior of ice and mechanical model and to analyze the factors and specific mechanisms (cutter's angle, rotation speed of the drill bit, and cutting depth) affecting cutting force for the rational design of ice core drill systems, improving the efficiency of ice core drilling and ensuring the drilling process runs smoothly. Therefore, in this paper, the process of ice cutting was observed, the fracture mechanics characteristics of the ice cutting process were analyzed, the formation process of ice chips was divided into three stages, and a mathematical model for the cutting force was established based on the observation results. The paper describes the damage conditions of ice failure and points out the factors and specific laws influencing cutting force. Furthermore, the cutting force generated under various experimental conditions was tested. Based on specified real-time variation curves of cutting force, the characteristics of cutting force were analyzed during the cutting and drilling process. Based on comparison to results of the average cutting force, the influence mechanism of various parameters acting on the cutting force was obtained. This proves the correctness of the mathematical model of the cutting force and provides a theoretical reference for the calculation of the cutting force during ice cutting and drilling in polar regions.

First-Principles Study on the Optoelectronic and Mechanical Properties of Lead-Free Semiconductor Silicon Perovskites ASiBr3 (A = K, Rb, Cs)

We deployed density functional theory to assess the structural, electronic, elastic, and optical properties of ASiBr3 (A = K, Rb, and Cs). KSiBr3, RbSiBr3, and CsSiBr3 band structure profiles suggest they are semiconductors with direct band gaps of 0.34, 0.36, and 0.39 eV, respectively. The material’s dynamic stability is evidenced by the formation energies acquired negative values (−2.35, −2.18, and −2.08 for K, Rb, and Cs respectively). Mechanical characteristics and elastic constants measured suggest the compound’s mechanical stability and ductile character, which was assessed by calculating the Poissons ratio (>0.25) and Pugh’s ratio (>1.75). The research also explores optical properties, including the dielectric function, refractive index, reflectivity, optical conductivity, absorption coefficient, and extinction coefficient for the optical spectrum. The findings highlight possible applications for these materials in the semiconductor industry and modern electronic gadgets. The optical properties assessment reveals that these materials have strong optical absorption and conductivity, making these compounds the best prospects for usage in solar cells. CsSiBr3’s lower band gap renders it the superior choice for light-emitting diode (LED) and solar cell applications. Our findings may provide a complete understanding for experimentalists to pursue additional research leveraging applications in LEDs, photodetectors, or solar cells.

Mechanical and vibrational behaviors of bilayer hexagonal boron nitride in different stacking modes

Hexagonal boron nitride (h-BN) is a semiconductor material with a wide band gap, which has great potential to serve as a nanoresonators in microelectronics and mass and force sensing fields. This paper investigates the mechanical properties and natural frequencies of bilayer h-BN nanosheets under five different stacking modes, which have been rarely studied, using molecular dynamics simulations. The mechanical properties, including Young’s modulus, the ultimate stress, ultimate strain, Poisson’s ratio and shear modulus, are studied for all five stacking modes. And the effects of strain rate, crystal orientation and temperature to bilayer h-BN nanosheets’ tensile properties have also been studied. Our findings suggest that bilayer h-BN nanosheets are basically an anisotropic material whose tensile properties vary substantially with stacking modes and temperature. Moreover, the natural frequencies are proposed in an explicit form based on the nonlocal theory. The differences of the fundamental natural frequencies among different stacking modes are affected by the constraint condition of bilayer h-BN sheet. The theory results match well with the simulation results. These findings establish elementary understandings of the mechanical behavior and vibration character of bilayer h-BN nanosheets under five different stacking modes, which could benefit its application in advanced nanodevices.

Investigation on the fracture mechanics characteristics and crack initiation of deep dense shale

The mechanical behavior of shale fractures significantly affects the structure and stability of hydraulic fracturing networks in shale gas reservoirs. Currently, there is insufficient research on the mechanical characteristics of fractures, crack initiation, and the prediction of fracture trajectories in deep dense shale. This study involved conducting direct tension, shear, and three-point bending fracture mechanical experiments on shale samples, complemented by numerical calculations and mechanistic analyses. The results show a significant influence of the bedding plane angle (γ) on the initiation properties and locations of shale fractures. With γ ranging from 0° to 90°, shale fractures transition from alignment with the bedding plane to penetration through it. Fracture initiation locations show a significant degree of randomness when fractures propagate along the bedding plane. The horizontal tensile stress changes with increasing γ, initially increasing and then decreasing as it moves away from the center. The evolution of the horizontal tensile stress field primarily causes alterations in shale fracture paths, reaching its peak value at γ = 45°. Shale initiation fractures can be classified into four types: tensile fractures through the bedding plane, tensile fractures along the bedding plane, shear fractures across the bedding plane, and shear fractures along the bedding plane. Established a criterion called the “maximum stress strength ratio” to determine fracture initiation, which can predict the initiation properties, locations, and paths of shale fractures. When γ is small, fractures mainly propagate along the bedding plane, with a higher likelihood of initiation occurring at the center of the specimen. Conversely, when γ is large, fractures mainly propagate through the bedding plane. The spacing of the bedding planes minimally affects the predicted fracture paths of shale. This study is of significant theoretical importance for reservoir stimulation and stability assessment in deep dense shale gas reservoirs.

A Lie group variational integrator in a closed-loop vector space without a multiplier

Abstract. As a non-tree multi-body system, the dynamics model of four-bar mechanism is a differential algebraic equation. The constraints breach problem leads to many problems for computation accuracy and efficiency. With the traditional method, constructing an ODE-type dynamics equation for it is difficult or impossible. In this exploration, the dynamics model is built with geometry mechanic theory. The kinematic constraint variation relation of a closed-loop system is built in matrix and vector space with Lie group and Lie algebra theory respectively. The results indicate that the attitude variation between the driven body and the follower body has a linear recursion relation, which is the basis for dynamics modelling. With the Lie group variational integrator method, the closed-loop system Lagrangian dynamics model is built in vector space, with Legendre transformation. The dynamics model is reduced to be the Hamilton type. The kinematic model and dynamics model are solved using Newton iteration and the Runge–Kutta method respectively. As a special case of a crank and rocker mechanism, the dynamics character of a parallelogram mechanism is presented to verify the good structure conservation character of the closed-loop geometry dynamics model.

Study on the influence of pore water pressure on shear mechanical properties and fracture surface morphology of sandstone

To further investigate the weakening effect of pore water pressure on intact rock mechanics properties and characteristics of fracture surface after failure, direct shear tests of sandstone were conducted under different pore pressure. A 3D scanner was employed to digitize the morphology of the post-shear fracture surface. The variogram function was applied to quantify the anisotropic characteristics of post-shear fracture surface. The relationship between deformation during shear failure of intact rock and quantitative parameters of fracture surface after shear failure was initially established. It can be found that amplitudes of the sinusoidal surface determine the maximum value of variogram, and period affect lag distance that reach the maximum value of variogram. Test results revealed that the increase of pore pressure has obvious weakening effect on shear strength and deformation of rock. Moreover, the increase of pore pressure makes the shear fracture surface flatter. It can be obtained that both Sillmax and Rangemax are positively related to shear strain, but negatively related to normal strain.

Green Synthesis of Dy2Sn2O7 Nanostructures Employing Gum of Ferula Assa Feotida for Formation of N3-substituted Quinazoline-2,4(1H,3H)- diones

Introduction: Dy2Sn2O7 nanoparticles (Dy2Sn2O7 NPs) were generated in the attendance of rheum gum, papaver somniferum gum, ferula assa feotida gum, barberry juice from Dy(NO3)3·5H2O and SnCl4·5H2O. Methods: The study of the structure of the specimens verified the generation of nanocatalysts in the scope of 20±5 nm. Synthesized catalysts with a variety of natural compounds were investigated by employing various methods. The characteristics of Dy2Sn2O7 were determined by SEM, TEM, EDX, and XRD. Due to the persistent colloidal stability, high mechanical, thermal sustainability, and high ionic internal character, the system can be deemed as an efficient catalyst by deploying the guest-host approaches. Results: Using industrial waste as raw materials and turning it into valuable products is an important phenomenon in green chemistry. Carbon dioxide is among these substances. This substance is less reactive and it is difficult to use them in a reaction. Conclusion: We announce the employment of CO2, isocyanides, and o-halo anilines in a multicomponent reaction for the production of quinazolines in the participation of Dy2Sn2O7 as a nanocatalyst.

Progressive damage and fracture behavior of brittle rock under multi-axial prestress constraint and cyclic impact load coupling

To explore the progressive damage and fracture mechanics characteristics of brittle rock materials under combined dynamic-static loading. Taking account of the coupling effect of the constraint states of uniaxial stress (σ1 ≥ σ2 = σ3 = 0), biaxial stress (σ1 ≥ σ2 > σ3 = 0) and true triaxial stress (σ1 ≥ σ2 ≥ σ3 ≠ 0) and impact load, the strain rate effect and prestress constraint effect of dynamic mechanical characteristics of sandstone are studied. The progressive damage evolution law of sandstone under the coupling of true triaxial stress constraint and cyclic impact load is discussed. The results show that with the increase of axial stress σ1, the dynamic compressive strength and peak strain gradually decrease, and the strain rate gradually increases, resulting in crushing failure under high strain rate. When the axial stress is fixed, the lateral stress constraint reduces the damage degree of sandstone and improves the dynamic compressive strength. With the increase of strain rate, the sample changes from slight splitting failure to inclined shear failure mode. Under the true triaxial stress constraint, the intermediate principal stress σ2 obviously enhances the dynamic compressive strength of sandstone. Under the constraints of triaxial stress, biaxial stress and uniaxial stress, the enhancement effect of dynamic compressive strength and the deformation resistance of sandstone are weakened in turn. Under the coupling of true triaxial stress constraint and high strain rate, sandstone samples show obvious progressive damage evolution effect under repeated impacts, and eventually inclined shear failure occurs, resulting in complete loss of bearing capacity.

Failure kinematics and mechanisms of the 2019 Yahuokou flow-like landslide along the Pingding-Huama fault in Zhouqu segment

Many large-scale landslides have occurred along the active Pingding-Huama fault in Zhouqu segment, Gansu, China. To better understand the failure mechanisms of these landslides, we use the Yahuokou landslide as a detailed case study. Field investigation was conducted to retrace the kinematics of the landslide and corresponding timeline of triggering mechanics. Dynamic triaxial tests were conducted to quantify the effect of rainfall and rockfall load on the physical and mechanical character of the landslide materials with in-situ stress level. Numerical simulation was used to evaluate the landslide stability under rainfall and rockfall load. The results show that a smaller initial rockfall of the limestone blocks along the upper headscarp of the landslide triggered a series of larger failure events that propagated through the greater landslide complex. We proposed that continuous rainfall and this rockfall load increased the pore water pressure and significantly reduced the shear strength parameters of the sliding materials. In addition, the rockfall load destroyed the structure of the shallow soil with buried depth <5 m, increasing the pore volume and water absorption capacity, which may cause the water content of the soil to exceed its liquid limit, and finally promoted plastic flow. Stability calculation further showed that rainfall alone was not sufficient to induce the landslide failure, but rather the coupled action of rainfall and rockfall load was needed. The conclusions drawn from this study outline complex failure mechanics of the Yahuokou landslide and may be helpful in understanding the fault-zone landslides widely distributed along the Pingding-Huama fault.

Numerical Simulation Study on the Mechanics and Pore Characteristics of Tectonically Deformed Coal under Multi-Level and Multi-Cycle Loading and Unloading Conditions

Horizontal well cavern completion and stress release is considered a potential technique for efficient development of coalbed methane in tectonically deformed coal (TDC). Pulsating loading and unloading is a key technique for the controlled expansion of caverns and broader stress release within the reservoir. However, current understanding of the mechanical characteristics and pore network structure evolution of TDC under cyclic loading and unloading conditions is still limited. This paper employs numerical simulation methods to study the mechanical behavior and damage characteristics of TDC under cyclic loading and unloading. After obtaining a set of micromechanical parameters reflecting the behavior of TDC samples under triaxial compression in high-stress states, the effects of different stress gradients and cyclic amplitudes on the stress–strain curve, porosity changes, and crack propagation in TDC samples were analyzed. The study results indicate that under various cyclic loading and unloading conditions, the mechanical response characteristics of TDC samples are broadly similar, primarily divided into compression, slow expansion, and accelerated expansion phases. Under low unloading level conditions, the volume expansion of TDC samples is minimal. Also, at the same unloading level, the strain increment decreases with an increasing number of cycles. Correspondingly, under these conditions, the porosity and microcrack expansion in TDC are less than in high-stress gradient scenarios. Under the same unloading level but different amplitudes, the volume expansion rate at 50% unloading amplitude is higher than at 1 MPa unloading amplitude for TDC, with an increased number of crack expansions. Therefore, under cyclic loading conditions, the sensitivity of crack propagation within TDC samples to amplitude is greater than that to unloading level. Under actual pulsating excitation conditions, a low-amplitude, low-stress gradient pulsation method should be used to maintain the stability of horizontal well caverns, and gradually increase the cyclic amplitude to achieve the efficient extraction of coalbed methane in TDC reservoirs. The findings of this study can serve as an important reference for optimizing process parameters in cyclic pulsating stress release engineering for TDC.

On the Origins of Randomness

AbstractThis paper is a concept paper, which discusses the definition of randomness, and the sources of randomness in the physical system (the Universe) as well as in the formal mathematical system. I discuss how randomness, through chaos, the second law, the quantum mechanical character of small scales, and stochasticity is an intrinsic property of nature. I then move to our formal mathematical system and show that even in this formal system we cannot do away with randomness and that the randomness in the physical world is consistent with the origins of randomness suggested from the study of mathematical systems. Rules and randomness are blended together and their interaction is shaping all observed forms and structures.