Special Relativity in Three-Dimensional Space-Time Frames

In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.

Teleportation of three-dimensional single particle state in noninertial frames

Considering the spin degree of freedom of the Dirac field, we study the entanglement behavior of a different class of communication channel and teleportation of three-dimensional single particle state in noninertial frames. Numerical analysis shows that the communication channel in our scheme can offer enough distillable entanglement for the teleportation protocol. Moreover, the teleportation protocol could work well if Rob＇s acceleration is not very big, but the fidelity of the teleportation is still reduced due to the Unruh effect.

NONLINEAR DYNAMICAL STABILITY ANALYSIS OF THE CIRCULAR THREE-DIMENSIONAL FRAME

The three-dimensional frame is simplified into flat plate by the method of quasi-plate. The nonlinear relationships between the surface strain and the midst plane displacement are established. According to the thin plate nonlinear dynamical theory, the nonlinear dynamical equations of three-dimensional frame in the orthogonal coordinates system are obtained. Then the equations are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundary conditions of fixed edges, then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimensional frame are studied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artificial method.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

Unique electromagnetic wave absorber for three-dimensional framework engineering with copious heterostructures

In order to obtain high-performance electromagnetic wave absorbers,the adjustment of structure and components is essential.Based on the above requirements,this system forms a three-dimensional frame structure consisting of MXene and transition metal oxides(TMOs)through efficient electrostatic self-assembly.This three-dimensional network structure has rich heterojunction structures,which can cause a large amount of interface polarization and conduction losses in incident electromagnetic waves.Hollow structures cause multiple reflections and scattering of electromagnetic waves,which is also an important reason for further increasing electromagnetic wave losses.When the doping ratio is 1:1,the system has the best impedance matching,the maximum effective absorption bandwidth(EAB max)can reach 5.12 GHz at 1.7 mm,and the minimum reflection loss(RL_(min))is-50.30 dB at 1.8 mm.This provides a reference for the subsequent formation of 2D-MXene materials into 3D materials.

Three-Dimensional Computed Tomography Assessment and Planning for Severe Lower Limb Deformities: A Case Report of Bilateral Fibular Hemimelia

To correct a lower limb deformity, orthopedic surgeons must have an exact understanding of the deformity. In general, preoperative planning is carried out using anterior-posterior (AP) and lateral radiographs. However, for severe cases with a combination of angular and rotational deformities of the lower limb, obtaining true AP and lateral radiographs is difficult and accurate calculation of the rotational deformity from radiographs is impossible. In this report, we propose to focus on preoperative assessment using three-dimensional (3D) reconstruction images of computed tomography (CT) scans for severe lower limb deformity in a patient with bilateral fibular hemimelia type II according to the Achterman- Kalamchi classification. She underwent bifocal deformity corrections of the bilateral tibiae using Taylor spatial frames in combination with the Ilizarov external fixator. Complete bony union was achieved, without angular deformity or limb length discrepancy.

Electrodynamics in Noninertial Reference Frames

The electrodynamics both in RF with prescribed law of motion and in FR with prescribed structure is considered. Parallel comparison for solutions in “uniformly accelerated” NRF M?ller system and in uniformly accelerated rigid NFR in the space of the constant curvature is carried out. The stationary criterion is formulated. On the basis of this criterion, one of the “eternal physical problems” concerning the field at uniformly accelerated charge motion is considered. The problems of electromagnetic wave spreading, Doppler’s effect and field transformations are discussed.

Reality of Space and Time

In Newton’s classical physics, space and time are treated as absolute, independent quantities and can be discussed separately. In Special Relativity, Einstein proved that space and time are relative and dependent and therefore must not be treated separately. Minkowski adopted four-dimensional space-time frames (4-d s-t frames), which indirectly revealed the dependency of space and time with the addition of a constraint for an event interval. We are not able to visualize 4-d s-t frames. Since space and time are inseparable, three-dimensional space-time frames (3-d s-t frames) can be constructed by embedding time into space to directly show the interdependency of space and time. Time contraction and length contraction can also be depicted graphically using 3-d s-t frames. We have much better understanding reality of space and time in 3-d s-t frames. This will lead to Contextual Reality for better understanding the universe.

Time, Length, and Mass Are Derived Quantities

Fundamental units of measurements are kilograms, meters, and seconds—in regards to mass length, and time. All other measurements in mechanical quantities including kinetic quantities and dynamic quantities are called derived units. These derived units can be expressed in terms of fundamental units, such as acceleration, area, energy, force, power, velocity and volume. Derived quantities will be referred to as time, length, and mass. In order to explain that fundamental units are not equivalent with fundamental quantities, we need to understand the contraction of time and length in Special Relativity. If we choose the velocity of light as fundamental quantity and length and time as derived quantities, then we are able to construct three-dimensional space-time frames. Three-dimensional space-time frames representing time with polar coordination, time contraction and length contraction can be shown graphically.