Eccentricity energy change of complete multipartite graphs due to edge deletion

The eccentricity matrix ɛ(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the eigenvalues of ɛ(G). Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such property. In this article, we give examples of graphs for which the eccentricity energy increase (resp., decrease) but the distance energy decrease (resp., increase) due to an edge deletion. Also, we prove that the eccentricity energy of the complete k-partite graph Kn 1, ... , nk with k ≥ 2 and ni ≥ 2, increases due to an edge deletion.

Nano-Sized Effect on Liquid Phase and Their Energy

Regardless of the state of matter, such as solids, liquids, and gases, the smaller the matter size from bulk to nano-scale, especially in the quantum region, the more rapid is the energy increase. To this end, this study introduces the concept of a group system, in which atoms behave as one, and this system is reinterpreted as that comprising temperature–entropy (TS) energy in thermodynamic data. Based on this concept, water was passed through various mesh-like dissolved tubes, where the size and energy of the water group system were observed to change. Thereafter, as the scale and number of the meshes increased, the ozone, chlorine, and oxygen constituents, which are closely related to sterilization and washing, are generated, changing the basic water composition. Thus, this nano-size impact is not limited to solids and could facilitate in revolutionizing the future applications in fluids.

Novel Design and Comparison of Structural and Modal Analyses of Auxetic Geometry versus Honeycomb Geometry

Auxetic structures are popular, since they have many applications in defense, textile and sport industries. The advantages of providing comfort and protection to people for the impact energy increase the usability of auxetic structures in these areas. Within the scope of this study, two structures were designed as honeycomb and auxtetic structures with lateral displacements in opposite directions. The auxetic and honeycomb structures were modeled in Ansys software by keeping the boundaries of these two structures close to each other. Structural and modal analysis were applied to these structures and the auxetic structure gave better results in terms of the tensile strength.

Increasing the CO2 Reduction Activity of Cobalt Phthalocyanine by Modulating the σ-donor Strength of Axially Coordinating Ligands

<p>Axial coordination of a pyridyl moieties to CoPc (either exogenous or within poly-4-vinylpyridine polymer) dramatically increases the complex’s activity for CO₂RR. It has been hypothesized that axial coordination to the Co active site leads to an increase in the Co dz² orbital energy, which increases the complex’s nucleophilicity and facilitates CO₂ coordination compared to the parent CoPc complex. The magnitude of the energy increase in the Co dz² orbital should depend on the σ-donor strength of the axial ligand—a stronger σ-donating ligand (L) will increase the overall CO₂RR activity of axially coordinated CoPc(L) and vice versa. To test this, we have studied a series of CoPc(L) complexes where the σ-donor strength of L is varied. We show that CoPc(L) reduces CO₂ with an increased activity as the σ-donor ability of L is increased. These observed electrochemical activity trends are correlated with computationally-derived CO₂ binding energy and charge transfer terms as a function of σ-donor strength. The findings of this study supports our hypothesis that the increased CO₂RR activity observed upon axial coordination to CoPc is due to the increased energy of the dz² orbital, and highlight an important design consideration for macrocyclic MN₄-based electrocatalysts.</p><p> </p><p> </p>

Increasing the CO2 Reduction Activity of Cobalt Phthalocyanine by Modulating the σ-donor Strength of Axially Coordinating Ligands

<p>Axial coordination of a pyridyl moieties to CoPc (either exogenous or within poly-4-vinylpyridine polymer) dramatically increases the complex’s activity for CO₂RR. It has been hypothesized that axial coordination to the Co active site leads to an increase in the Co dz² orbital energy, which increases the complex’s nucleophilicity and facilitates CO₂ coordination compared to the parent CoPc complex. The magnitude of the energy increase in the Co dz² orbital should depend on the σ-donor strength of the axial ligand—a stronger σ-donating ligand (L) will increase the overall CO₂RR activity of axially coordinated CoPc(L) and vice versa. To test this, we have studied a series of CoPc(L) complexes where the σ-donor strength of L is varied. We show that CoPc(L) reduces CO₂ with an increased activity as the σ-donor ability of L is increased. These observed electrochemical activity trends are correlated with computationally-derived CO₂ binding energy and charge transfer terms as a function of σ-donor strength. The findings of this study supports our hypothesis that the increased CO₂RR activity observed upon axial coordination to CoPc is due to the increased energy of the dz² orbital, and highlight an important design consideration for macrocyclic MN₄-based electrocatalysts.</p><p> </p><p> </p>

Increasing the CO2 Reduction Activity of Cobalt Phthalocyanine by Modulating the σ-donor Strength of Axially Coordinating Ligands

<p>Axial coordination of a pyridyl moieties to CoPc (either exogenous or within poly-4-vinylpyridine polymer) dramatically increases the complex’s activity for CO₂RR. It has been hypothesized that axial coordination to the Co active site leads to an increase in the Co dz² orbital energy, which increases the complex’s nucleophilicity and facilitates CO₂ coordination compared to the parent CoPc complex. The magnitude of the energy increase in the Co dz² orbital should depend on the σ-donor strength of the axial ligand—a stronger σ-donating ligand (L) will increase the overall CO₂RR activity of axially coordinated CoPc(L) and vice versa. To test this, we have studied a series of CoPc(L) complexes where the σ-donor strength of L is varied. We show that CoPc(L) reduces CO₂ with an increased activity as the σ-donor ability of L is increased. These observed electrochemical activity trends are correlated with computationally-derived CO₂ binding energy and charge transfer terms as a function of σ-donor strength. The findings of this study supports our hypothesis that the increased CO₂RR activity observed upon axial coordination to CoPc is due to the increased energy of the dz² orbital, and highlight an important design consideration for macrocyclic MN₄-based electrocatalysts.</p><p> </p><p> </p>

Jet-driven bow waves as electron accelerators in the magnetosheath: Monte Carlo simulations

&lt;p&gt;Magnetosheath jets are fast flows of plasma frequently observed downstream of the Earth's quasi-parallel shock. Previous observations have shown that these jets can exhibit supermagnetosonic speeds relative to the background flow and develop their own bow waves or shocks. Such jets have been observed to be able to accelerate ions and electrons. In our study, we model electron acceleration by jet-driven bow waves in the magnetosheath using test-particle Monte Carlo simulations that include magnetic mirroring and pitch-angle scattering of magnetic irregularities. We compare the simulation results to spacecraft observations of similar events to understand the acceleration mechanisms at play. Our preliminary results suggest that the energy increase of electrons can be explained by shock drift acceleration at the moving bow wave. Our simulations allow us to estimate the efficiency of acceleration as a function of different jet and magnetosheath parameters. The acceleration introduced by jet-driven bow waves amplifies shock acceleration downstream of the Earth&amp;#8217;s bow shock and may also be applicable to other shock environments.&lt;/p&gt;