In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

One of the main issues involved during tunnel construction with tunnel boring machines is the tail gap grouting. This gap is between the external diameter of tunnel lining and the excavation boundary that is filled with high-pressure grouting materials. In this work, three different approaches of gap grouting modeling in the FLAC3D software are investigated with a special attention to the influence of the grout material hardening process. In the first approach, the grout is modeled as a liquid during injection, and considering the TBM advancement and its hardening time, the grout characteristics are changed to the properties of the solid grouting. In the second approach, the grouting material from the beginning of injection is considered with the properties of solid grouting in the model, and the liquid phase is ignored. In the third approach, without considering the back-filled grouting area in the model geometry, only the injection pressure is applied to the end of the shield and behind the installed segments. The validity of the approaches is evaluated with respect to the maximum ground surface settlement. All the three approaches estimate different surface settlement but the result of the first approach is closer to the monitoring data. Also as a sensitivity analysis, in this work, we investigate the effect of the elastic modulus of liquid and solid grouting materials on the amount of surface settlement that can help to gain a more accurate insight into the effect of grout mixture.

Nonlinear equations frequently arise in the analysis of statistical mechanics models, particularly in mean-field theories where self-consistency relations govern macroscopic order parameters. In this paper, we revisit the classical self-consistency equation for the magnetization of the Ising model in mean-field approximation. We analyze its solutions, discuss iterative and numerical approaches, and illustrate how the behavior of solutions reflects the underlying phase transition. Our results demonstrate the interplay between nonlinear analysis and physical interpretation, highlighting the universality of such equations in statistical systems.

In this work, we investigate a non-linear differential equation relevant to the computation of entanglement entropy in interacting quantum systems. We do this, inspired by field-theoretic and holographic models, we introduce a simplified equation to describe the entropy as a function of subsystem size and coupling strength. By comparing analytical approximations with numerical solutions, we uncover a crossover behavior between area-law and volume-law regimes, which are key features of entanglement dynamics in quantum systems. This minimal model captures the essential non-linear structure underlying entanglement growth, offering insights into the interplay between subsystem size and interaction strength. Our findings provide a framework for understanding the transition between distinct entanglement scaling laws, bridging theoretical predictions and numerical observations. This work highlights the utility of simplified models in exploring complex quantum phenomena and contributes to the broader understanding of entanglement dynamics in interacting systems, with potential applications in quantum information and condensed matter physics.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

Plastic hinge properties play a crucial role in predicting the nonlinear response of structural elements. The plastic hinge region of reinforced concrete normal beams has been previously studied experimentally and analytically. The main objective of this research is to evaluate the behavior of the plastic hinge region of reinforced concrete deep beams and its comparison with normal beams through finite element simulation. To do so, ten beams contain six deep beams, and four normal beams, under concentrated and uniformly distributed loading, are investigated. Lengths in the plastic hinge region involving curvature localization, rebar yielding, and concrete crushing zones are studied. The results indicate that the curvature localization zone is not suitable for the prediction of plastic hinge length in reinforced concrete deep beams. Based on the results it can be stated that in simply supported normal beams the concrete crushing zone is focused on the middle span, but in simply supported deep beams by creating a compression strut between loading place and support, the concrete crushing zone spreads along the compression trajectory. The rebar yielding zone of simply supported beams increases as the loading type is changed from the concentrated load at the middle to the uniformly distributed load.

We investigate nonlinear differential equations arising in holographic models of black hole spacetimes within the AdS/CFT correspondence. Emphasis is placed on analytical approximations and numerical solutions of scalar perturbations and nonlinear wave equations in asymptotically anti-de Sitter black holes. We show how effective potentials lead to boundary value problems governed by nonlinear ordinary differential equations. Analytical methods, such as matched asymptotic expansions and perturbative ans"{a}tze, are compared with spectral numerical approaches. Applications to holographic thermalization, quasinormal spectra, and cosmological analogues are discussed. Our results highlight the interplay between nonlinear analysis and physical interpretation in string-inspired models of gravity.

This study, investigates the factors impacting on sloshing phenomenon of the tank structures including geometry, burial rate, and installation of T-shaped baffles under two different earthquake records. The results indicate that the tanks with larger dimensions will experience less sloshing height. Moreover, length, height, and the freeboard, respectively, are effective in lowering the roof force. However, freeboard plays a more important role comparing with the burial rate of the tank in reducing the roof force. Note that as the freeboard and burial rate increase, the roof force decreases. The results represent that decreasing the height to length ratio of the tank reduces the maximum sloshing height. Finally, using the energy dissipation ratio concept, it is observed that the tank with baffles shows much better performance with the energy dissipation ratio of about 96%, comparing with the burial approach in which even the tank under 100% burial rate just dissipates less than 50% the energy induced by the sloshing waves.

Because physical changes are calculabe within mathematics by means of equations and especially because for a model designer these equations are of a "partial differential" sort and are often not "analyzable", the importance of their numerical solution is rendered ever more conspicuous not only from a practical (and algorithmic) standpoint but also "from a theoretical perspective. There are two general ideas, namely "finite differences" and "finite element", involved in solving all kinds of these equations. It is decided to use only the finite differences, for their simplicity and comprehensiveness, in the investigation of the solution to the "parabolice" variety of these equations, which in turn entail more diverse methods such as "explicit" and "implicit" approaches, before finally comparing and contrasting these methods from the point of view of accuracy, time of application, and writing a computer program.