School of Biological and Physical Sciences

Mean Gravitational potential energy of neutrons in isothermal neutron-star atmospheres: a statistical-mechanical approach

2026-09-10T07:54:53Z

Mean Gravitational potential energy of neutrons in isothermal neutron-star atmospheres: a statistical-mechanical approach Maritim, J. K.; Rotich, S. K. We develop a statistical-mechanical derivation of the mean gravitational potential energy per particle in an infinitely extended isothermal atmosphere and establish the precise domain in which the result ⟨𝑈⟩ = 𝑘𝐵𝑇 can be used as a benchmark for compact-star surface layers. The classical model assumes a dilute, non-degenerate, non-interacting gas in plane-parallel geometry, constant temperature, and a locally uniform gravitational acceleration. Direct integration of the Boltzmann distribution and the canonical partition function both yield ⟨𝑈⟩ = 𝑘𝐵𝑇 and a scale height 𝐻 = 𝑘𝐵𝑇/(𝑚𝑔). For a canonical 1.4 M⊙, 12 km neutron star at 106 K, the Newtonian and local general-relativistic surface gravities are 1.290e+12 and 1.594e+12 ms⁻², respectively, giving free-neutron benchmark scale heights of 6.388 and 5.172 mm. Because H/R ≈ 4.31e-07, the local constant- gravity and plane-parallel approximations are geometrically well motivated, although the absolute surface gravity requires relativistic correction. The Maxwell–Boltzmann validity domain is quantified using the thermal de Broglie wavelength and neutron degeneracy parameter 𝑛𝜆𝑇³ ; at 106 K the conservative 𝑛𝜆𝑇³ = 0.1 boundary occurs near 3.2 × 104 𝑔 𝑐𝑚⁻³ for an ideal free-neutron gas. We then separate this dilute benchmark from the strongly degenerate crust and core, introduce relativistic Fermi energies, and formulate the Tolman– Oppenheimer–Volkoff equations required for global stellar structure. Comparison with established neutron-star atmosphere calculations shows that the analytical result is best interpreted as a limiting hydrostatic/statistical- mechanical benchmark, not as a complete photospheric model. The formulation therefore provides a transparent bridge from elementary statistical mechanics to relativistic compact-star physics.

Nutrient budgets for sustained crop production in African soils: evidence from potato-grown soils in Tanzania

2026-08-26T13:30:37Z

Nutrient budgets for sustained crop production in African soils: evidence from potato-grown soils in Tanzania Aloo, Becky Nancy; Tripathi, Vishal; Makumba, Billy Amendi; Mbega, Ernest Rashid Soil fertility is under pressure worldwide due to agricultural intensification to match food demand. In sub-Saharan Africa (SSA), the depletion of soil nutrients is the root cause of the widespread food insecurity. Therefore, there is a need to continually monitor soil nutrient levels to drive policies and management options for sustained food production. Compared to other crops, potato (Solanum tuberosum L.) is increasingly becoming significant for food and economic security in SSA. The crop is, however, a heavy nutrient feeder and withdraws hefty amounts of nutrients from the soil which can interfere with its sustained production. However, very few studies have assessed the soil fertility levels of potato-grown soils in different parts of SSA. This chapter includes a case study report from the investigation of the fertility status and associated physicochemical properties of potato-grown soils in various agro-ecological areas in Tanzania. Soil samples collected from 27 potato farmlands were sampled in nine districts and analyzed for pH, electrical conductivity at 25 °C (EC25), soluble salts (SS), particle size distribution, potassium, phosphorus, iron, nitrogen, zinc, organic matter (OM), and organic carbon (OC) using standard methods. The results revealed significant differences for fertility-related physicochemical properties like EC25 (P = 0.004), (%) SS (P = 0.004), (%) OC (P = 0.018), and (%) OM (P = 0.019) in the soils but there were no significant differences for the fertility status of soils across the different study areas. Significant (P < 0.05) correlations were also observed for different parameters. The study concluded that specific soil characteristics differed significantly while fertility was relatively consistent. These findings serve as a basis for comprehending the existing soil conditions and can inform future strategies for sustainable soil management to ensure optimal nutrient levels to support the continued productivity of potatoes in the region.

All optical polarization-based and DSP-Assisted distributed fiber sensor for earth mass movements caused by environmental factors

2026-08-24T08:04:43Z

All optical polarization-based and DSP-Assisted distributed fiber sensor for earth mass movements caused by environmental factors Kipnoo, Rotich E.K; Isoe, G.M.; Kiboi, Boiyo c; Kuja, S.; Waswa, , D.; Leitch, A.W.R. Fiber optic sensors for industrial, consumer, medical and military applications have been reported. Their working principle is majorly based on non-linear optics. For the first time to our knowledge, we propose a cost-effective real time monitoring polarization-based digital signal processing (DSP)-assisted sensor that relies on linear optics for application in earth mass movements due to environmental factors. A sensitivity of 0.075 kg−1 is achieved. This is realized on an average SOP speed of 0.83°/s yielding 598° angular drift on its polarization changes. A sensing performance comparison of single mode fiber (SMF) and large effective area fiber (LEAF) fiber is reported.

Tunable Phase Shifters for 6G Beamforming Networks

2026-08-24T07:41:08Z

Tunable Phase Shifters for 6G Beamforming Networks Naibei, Victor Chepkech; Choge, Dismas; Jena, James; Waswa, David; Boiyo, Duncan Kiboi The deployment of 6G network requires multiple number of antennas at the base station with multiple signals that undergo constructive interference to create thinner beams with more energy so as to mitigate path loss. This will support higher data rates, lower latency levels, and improved energy efficiency. This paper proposes a phase-shifting technology for beamforming that focuses radio energy to a specific user equipment, thus maximizing spectral efficiency. We present a novel approach of phase-shifting technology by generating tunable microwave pulses using the slicing-level technique in an optoelectronic oscillator (OEO) setup. Two laser sources undergo intensity and phase modulation using a well-characterized Mach–Zehnder modulator and a phase modulator. Modulating signals in the range of 100 kHz–13.3 MHz are used to generate microwave waveforms. Repetition-rate-tunable pulses are generated from the microwave waveforms using the slicing-level technique. Photonic-assisted tunable pulses generated have a pulse width ranging from 0.6 ns to 7.5 μs and a duty cycle ranging from 17% to 96% optimized for phase shifting (𝜑) of signals, with potential for multiple antenna elements, which act as time delays aimed at creating constructive interference of the beams that form a concentrated beam of energy. This work successfully creates phase shifters ranging from 14° to 299° that can be used to steer antennas for 6G network by controlling pointing angles at the antenna array terminals, which creates a multiplex transmission line as a linear combination of signals.